Does anyone know whether this sort of music reflects the widely published editions of the past (e.g., of the 1800s), or whether it might have been a regional style?

Note shapes indicated stressed-long versus unstressed-short syllable-note values. I'm sure that we must have someone on the forum who is more learned than I about this subject.

Exactly. See the first page of Jeff Ostrowski's article on the Rhythm of the Vatican Edition:
http://www.ccwatershed.org/media/pdfs/13/08/17/14-49-29_0.pdf

raph, I'm not aware of a Kyriale specific to this region, but you may find some resources at: https://schola-sainte-cecile.com/tag/plain-chant-picard/

I did a search on the French term (épître farcie) and found a few hits including this definition:

Stuffed Epistles , a name given during the Middle Ages to the epistles of certain solemn Masses, the verses of which were sung alternately in Latin and in rhymes of the vulgar tongue. This word comes from the Latin stuffed (stuff, fill, intermingle). Father Leboeuf inserted seven in his historic treatise on ecclesiastical chant . Fétis ( Revue de la musique religieuse , 1846) reported many other stuffed pieces that were sung in the churches : some remained in use in Aix , Dijon , Rheims , etc., until the XVIII th century. (P.).

That might be the best way to search further on this topic.

For the original site (in response to the OP), I was suggesting that they may be familiar with other resources (including printed books) of chants from this style since there are several examples on the page. I would see if I could contact them - perhaps via their facebook page. I didn't explore, but they list an area for liturgical music books in PDF as well as related blogs and other potential resources.

...would have been...

Mr Hawkins asks if this is how Sarum chant would have been heard by Henry VIII, the Bad. Yes, it very likely would have been quite similar. Indeed, it is not altogether dissimilar in notation or performance to post-Tridentine Medicean chant, which (but for the savaging of melismae) likely reflects to some degree an earlier praxis. If one listens even today to Orthodox chanting there is a similarity to the long-short syllabification of our example. Something about this style, to settle on strong syllables and skip over weak ones, just seems to be 'human nature' and reflects habits of normal speech. One has, even in the reading of the Lectionary at mass, to train people not to do this, but to give articles and prepositions and weak syllables their due. Without doing so the reading or chanting will be unintelligible.

An afterthought in the form of a question - does this style of singing chant bear a resemblance to the semiological approach with its emphasis on textual rhythms rather than the melodic emphasis of pre-Cardinian Solesmes chant?

Further, there is now, I think, a scholarly consensus that plainchant hymnody was sung typically with short-long (or long-short) values corresponding to the metre of the verse texts. (This may [or may not, probably not?] be a 'hold over' from normal classical Latin speech patterns, in which stress, accent, was enunciated as length, not vocal intensity.)

I don't know if anyone might still be interested in this (since, it's a few months old), but I found the book that this is in on Google Docs: "Paroissien note en plain-chant a l'usage du clerge et fideles du diocese d'Amiens..." (There is also a republication available on Amazon.)

HERE