I'm sorry, let me be more direct:

How the organ accompaniments from Fontgombault Abbey recordings, like on Easter mass, are made?

1. They sound different from most of the accompaniments I have found, like the ones from Commitante Organo;

2. Do they play the melody? I can hear high notes, but can't tell if is an chord or the melody played along;

3. I found René Livron's "Accompagnement du kyriale grégorien" and they're quite similar, but Fontgombault play a root note an octave lower when the full choir enters.

I would ask the abbey directly by email; you can send the email to the secretariat, but ask for the choirmaster. Fontgombault, Triors, and Clear Creek are all reachable via email; I don't know about Randol, and I don't know if Wisques adopted the Fontgombault style when it was repopulated.

Thanks as usual to Dr. Weaver. I would add that Fr. Bachmann once wrote an accompaniment for me (we wound up going with the Solesmes version anyway), for the Ave Maris Stella in Sabbato (NB: the monastic version has one note with an episema, but it's a dotted punctum in the Roman office). He told me to play the alto in the right hand or omit it and to double, at the octave below, the bass if you have a pedal (so he clearly envisions this being played on manuals without a pedalboard!)

I think that this concurs with Dr. Weaver's interpretation of how one might need to do the chironomy in the right hand.

My thoughts, as a non-organist who is terribly interested in the Fontgombault/ICRSP/Schola Saint-Grégoire tradition as well:

Clear Creek, a daughter house of Fontgombault, does use the accompaniment for the Liber Cantualis, at least from time to time, for chants in that book.

I don't know if the propers are routinely sung with organ or not from the volumes of the Graduale Romanum containing accompaniment or if they have a notated gradual for this purpose.

The files here give a very good impression; you can actually hear the organ clearly (on my computer, at least… I'm often listening in the car).

It's true that they omit the melody, but you could play it without much difficulty.

(This is both for Soneto and those who don't know the style. It's been mentioned before, but it's worth exploring again.)

The office accompaniment is given first, in the antiphonal itself, with a key signature, e.g. "4 fb". The first note is explicitly named, e.g. "Fa" (F); now, we can say that it is F minor, but I don't dwell on it too much unless I'm explaining a full accompaniment to my organist. A series of note names, numbers, and symbols underneath the square notes tells the organist what chords to play and what to change. The older (1930s) Solesmes-style accompaniments changed the bass note only on the ictus, and my example has changes only on the ictus as well, but somewhat less frequently. Triors described this style as "lourd" (heavy) and while I agree, it's pleasant in its own way; people are too dismissive of this because it's not pure modality, which doesn't respect the amount of work and love for chant done by organists such as Henri Potiron whose collections are now scanned and available online.

The notation is not terribly intelligible without being taught directly, and you can see in the attachment (the scan of the Antiphonale monasticum) that while the hymn has its own range unrelated to the psalms, the Magnificat antiphon on the subsequent page has B-flat as the dominant (Fa) which would certainly be the case in France, but Clear Creek apparently uses A. In either case, the principles be should the same.

Anyway, you can compare the singing here (as far as I can tell) unaccompanied to their antiphonal and the version which Fr. Bachmann wrote for me (with one sharp, not four flats!).

I made this quick sheet of what I can hear from Fontgombault's Ave Maria...Virgo serena Seq. and played it with a simple Gedeckt 8' on Musescore. Yes, from what I could hear, they did parallel fifths.