Do you live in Pointe Coupee? If so you should look up this family in the Catholic Church Records by Diocese of Baton Rouge. The Majors married into my family way back when, and I can find just about all I need in these 18 volumes.
The Majors of LA began with Etienne Bosseron dit Major, I am convinced.
If your local library doesnt have these books, the state library on Bluebonnet Dr in Baton Rouge has a huge gene section. It's very good.