garstonite - it's not on geneanet, it's a link to an external website, probably run by one of the local genealogy groups who do transcriptions.
Be careful of submitted information on Ancestry - his son cannot possibly have been born Birmingham, Alabama in 1761 as Birmingham was a post-civil war town founded 1871.
There was, however, a French presence in the area right up to 1763 (Treaty of Paris), centred on what is now Mobile, Alabama. Some history/background reading:
http://en.wikipedia.org/wiki/Fort_Condehttp://en.wikipedia.org/wiki/Fort_Toulousehttp://en.wikipedia.org/wiki/Fort_TombecbeYou should 1) confirm the name and birthplace of the son b. 1761, and then 2) look for Catholic parish records for that area, if they survive.
Also, do you know if the family stayed in the area after 1763, or did they move elsewhere?