MJO is absolutely right. I haven't dug extensively into these rites, but it would probably be more accurate to refer to them as the Gallican Uses, which is to say, the local usages of the Churches of Gaul. One such being the Use of Lyons. The best comparison is probably to the Sarum Uses, with which many elements were shared, such as tropes, proses, sequences, etc. but with localized texts and feasts—or with the Dominican Rite in certain cases. Again, as MJO said, that's a very different thing than the Gallican Rites which were distinct rites from the Roman Rite, as opposed to local usages of it, having different structures and many different Eucharistic prayers for example.

It's a shame these amazing medieval liturgies lasted so long only to be quashed by a wrongheaded ultramontanism based on bad history.

From what I understand there is a distinction between the ancient Gallican Rite (as found in the Carolingian age, the Gallican Rite(s) as the evolved during the Middles Ages, and the Neo-Gallican Rites which emerged in the 18th Century.

From what I understand (and please correct me if I am wrong):

The ancient Gallican Rite is basically the Mass that was to become the 'Roman Rite' as we know it today: Liturgical history seems to show that there was a Roman and a Gallican Rite: Charlemagne wished to remold the liturgy of Gaul to conform more to Roman Practice, and so he ordered copies of the Roman liturgical books, etc., and imposed them on his realm; However, their imposition (including that of the Chant) was heavily Gallicanized by the local clergy, this Carolingian rite then traveled back across the Alps, in turn heavily influenced the Roman Rite. This Romano-Gallican Rite flowered considerably in the Middle Ages, having spread throughout Europe, and blossomed into the various local usages such as Paris, Lyons, Salisbury, etc., including the Missal or the Roman Curia, used as the basis of the Tridentine Reform. These Rites (Sarum, Paris, Lyons, etc.) on account of the proviso of the Council of Trent could, and did, legitimately continue (just as the Sarum Rite would have if the English Reformation had not taken place); which would account for the late date of Richelieu's 'Tridentization' of the Church in France.

After the Tridentization of the French Church, there was the Gallican Movement, which sought to bring greater control of the French Church to the French Bishops and the French Crown: the result of this was the re-gallicanization of the Tridentine Rite, the re-incorporation of certain Mediaeval Customs, etc. This created the Neo-Gallican Rites, of which basically every City with a Cathedral had one: of them all, the ones to most closely stick to an authentic Mediaeval predecessor were the Neo-Gallican Rites of Paris and Lyons (which basically revived the Old Missals, with some Tridentine accretions). Other Neo-Gallican Rites include Amiens and Versialles. The marks of many of these liturgies include stational processions (with proper Antiphons, Verses, and Collects) before the Principal Mass on Sundays and Holy Days; often different chants from the corpus of Gregorian Chant (though Paris and Lyons are near perfect matches to the Roman Rite); many local festivals; choir ceremonial, such as rulers of the choir in cope, which are not in the Tridentine Rite (because the Curial Missal was primarily intended for Low Mass); multiple sacred ministers (at least in Cathedrals and Collegiate Churches) at Solemn Masses; the blessing of the Antidoron after Mass; the singing of Terce before the Solemn Mass; and, more importantly, the liberty for parishes to incorporate as much or as little of the Missa Solemnis as is feasible for their means (i.e., a Missa Cantata with priest and two servers without incense would not preclude the cantors from vesting in cope, etc.). Some of these 'Gallican' features can actually still be seen in the Masses at St. Eugene in Paris with Henri de Villier's schola.

Unfortunately, in addition to the wonderful (and in many cases authentic) liturgical mediaevalisms of the Neo-Gallican liturgies, some were also influenced by Jansenism. It was the Janesnistic influence which caused the 19th century Ultramontanists like Gueranger to push for the implementation of the Tridentine Mass throughout France. In many cases they won--but the Lyonese Rite lasted until Vatican II. Below is a photo of Nuncio Angelo Roncalli celebrating the Pontifical Mass according to the Rite of Lyons.

And Solemn Mass according to the Rite of Versailles

Anyway, it’s interesting so keep the comments coming. I’m not personally proposing to restore these rites so I don’t see how there can be any controversy.

Sad it is that VII denuded us of the unimaginable richness of liturgy and the depths of its metaphor and symbolism with respect to the Biblical references and ritual with apostolic roots. It would appear, though, that Trent itself did its share of denuding. It is an historical truism that one generation's valued and highly symbolic tradition is the next's meaningless accretion. The suppression of sequences is but one example. Once potent extensions of the jubilus and bearing an intentionally imagined likeness to the angelic choirs and their ecstatic praise beyond human speech, Trent left a meagre five of these to be sung with a jubilus but no jubilation, nor any hint of ecstasy. Now, the richness of meaning these hymnodies once carried, putting every celebration in its ontological context, is replaced by a barren absence of jubilus or jubilation, and a rare sequence which is likely to be read (yes, unimaginable as it is, they actually read it!) in mumbled tones by the 'community' instead of being inspiredly rendered by skilled cantors and choirs singing their verses alternatim - all the while wearing copes.
And now our people stand there and mumble sing without a hint of jubilation their cute little dance-like and jubilusless triple alleluya with an undembarrassedly straight face.

Those interested in mediaeval liturgy, and sequences in particular, may consult and/or acquire Gothic Voices, by Margot Fassler, Notre Dame U Press. I recommend this book highly.

All that cloth of gold, and that plethora of dalmatics, tunicles, and copes in the Rite of Versailles that Salieri shows us above is very impressive and beautiful to see - but they aren't wearing apparelled albs and amices!

Well, let us know when you have recaptured the escaped name.
Um, would it be A Sense of the Sacred: Roman Catholic Worship in the Middle Ages?

There was a few months ago an extended facebook thread on Kwasniewski’s page on this topic.
My doctoral document dealt with mid-nineteenth century France.
Gueranger was of the opinion that the Gallican rites, composer in the 17th and 18th centuries, were thoroughly inspired by Enlightenment rationalism and were not reflective of true Catholic Tradition. These books principally differed from Roman books in the Divine Office and in rubrics for mass. Guerangers solution to all problems though was to appeal to Rome and make things more Roman. He was one of the strongest ultramontanists.
As we can see from the current pontificate, ultramontanism poses lots of problems. In the 19th century, ultramontanists used a lot of politics and underhanded methods to force bishops to give up their local uses and adopt the Roman books.

This connects with music in two ways:
1. The gallican uses called for organ versets. The Tridentine did not. Thus, organ versets, the primary function and tradition of French organists, disappeared within a decade.
2. Roman use had a heavier insistence on chant. Ultramontanists places a lot of pressure on adopting chant especially as performed by Gueranger’s Solesmes.

To be fair, French liturgy and liturgical music needed reforming. The Revolution had wrecked all French church institutions, not to mention society at large.

Indeed, I would also argue that the Tridentine "reforms" largely consisted of imposing Low Mass liturgical practices and principles upon the entire Roman Rite. I mean, when you look at the splendor and liveliness of the various medieval Uses of the Roman Rite, which would have been the liturgical norm in literally every single place in Western Europe outside of Rome (specifically the papal chapel), it becomes apparent that Trent actually did considerable damage to the liturgy. An unpopular opinion, especially in some traditional circles, but one that is based upon a large body of demonstrable facts.

Whether it is the glorious poetry of Sequences, the profound expository prose of the Tropes upon the antiphons and responsories of Mass and Divine Office, the hundreds of proper offices of saints appointed for the Divine Office, or the many and varied customs of medieval cathedrals......the loss is staggering when one actually takes the time to do the math. Thousands upon thousands of sacred chants were abruptly and quite arbitrarily removed from the Roman Rite, along with a lot of very ancient ceremonies.

An academic specialist of medieval liturgy told me once that if I wanted to have a glimpse of the overall look of the liturgy in French cathedrals during the middle ages, I should go to a service in an English, Anglican cathedral. He was no tridentinist at heart.

Trent was late implemented in France for several reasons : first the Religions Wars lasted till the end of the 16th century ; then the Catholic party wanted that Trent decrees be registered as French law by the Parliament, which the King Henri IV did not want for obvious reasons of independence of the secular realm, so he prohibited the implementation of the council altogether. His wife maintained this policy during her regency over Louis XIII.

It is only when Cardinal de Richelieu, minister for Louis XIII, had definitely delt with the Protestant party (at the siege of La Rochelle) and gotten some independence towards the Catholic party (called the "Devout Party") during the "Journée des dupes", that he could allow the decrees of the council to apply in French dioceses.

The "Devout Party" then organized itself in "Compagnie du Saint-Sacrement". It was during 36 years an influential force : its members, aristocratic and wealthy, paid for the creation of seminaries, and of the "Missions étrangères de Paris", but also worked towards censorship of Molière and the internment of the poor or mentally ill in the "Hopital général", leading to a lot of stigma for mental illness that still exists in France.

Surely the French Organ Mass, and its predecessors, was for a sung Low Mass? And after 1570 Byrd cannot have expected ever to have gathered three priests for a Solemn Mass , so again sung Low Mass, possibly Sarum.
By the restablishment of the hierarchy, and liberation from the control of Propaganda, Wiseman was under the ultra-montanist spell of W G Ward (whom he appointed as professor of moral philosophy and then to the chair of dogmatic theology at his seminary, in contravention of Canon Law) so the Sarum protagonists had little chance.

sung Low Mass

@a_f_hawkins and @tomjaw By this do you mean a Low Mass with music as we know it today, with items other than the propers and ordinary sung, or do you mean something bridging the gap between a modern-day Low Mass and Missa Cantata? I guess you must mean the latter re. Byrd, considering his Gradualia and three masses.

He obviously was able to find a choir, and they would probably have been some kind of minor order.

On the contrary, we have documentary evidence from either Byrd or an associate of his (I can't quite remember) praising the voices of his patron's daughters, who managed quite well with the treble parts.

Wikipedia has an article on the French Organ Mass. It begins

The French Organ Mass is a type of Low Mass that came into use during the Baroque era. Essentially it is a Low Mass with organ music playing throughout: part of the so-called alternatim practice.

This intro seems to have been unchanged since 2005, although the rest of the article is quite different. If it is erroneous perhaps someone with more knowledge than I have would correct it (anybody can change it, and an editor can change it back if they see fit).

Were these different manifestations at different times, Baroque v. 19th century? I saw, but can longer find, the suggestion that Louis XII who insisted that the O salutaris ... be sung at the elevation, preferred Low Mass; and that essentially he imposed some form of Missa Cantata on the royal chapels.

Were these different manifestations at different times, Baroque v. 19th century? I saw, but can longer find, the suggestion that Louis XII who insisted that the O salutaris ... be sung at the elevation, preferred Low Mass; and that essentially he imposed some form of Missa Cantata on the royal chapels.

Definitely. You're correct about Louis XII prescribing the O salutaris at the Elevation. Supposedly the Ave verum corpus had been sung there in former times. As for Low Mass being preferred by the kings of France, that was certainly the case later. Google "solemn low mass" and you'll get a result from Music in the Seventeenth Century by Lorenzo Bianconi, which discusses the function of the grand motet in that context - cf. the works of Clérambault. I wonder if there may have been a prohibition against women's voices at High Masses that wasn't enforced for Low Masses.

From Fr. Anthony Ruff's Sacred Music and Liturgical Reform: Treasures and Transformations. My apologies for the highlighting! Considering that the polyphonic Sanctus and Benedictus were already separated in the 16th century, it seems probable that "at the Elevation" meant during the Consecration, not afterward. Of course, when the Sanctus is sung in Gregorian chant, it is lawful to sing a motet in honor of the Blessed Sacrament after the Consecration, but I don't think that's the practice under consideration here.