Here’s my understanding as a native Texan with examples (don’t take this too seriously):

Y’all -> group of people (howdy yall)

All y’all -> everyone (all yall need to listen up!)

All’s yall -> only thing (alls yall need is another beer)

All y’all’s -> singular possessive of everyone’s stuff (put all y’all’s shit away)

All’s y’all’s -> plural possessive of everyone’s stuff (alls y’all’s cars are blocking me in). This one is a bit awkward and most people just use all y’all’s instead

It's not French!

Hmm. Maybe in https://en.wikipedia.org/wiki/Paris,_Texas?