There has never been a civil parish named St. Antoine, nor was there a "regional" church parish that served that function prior to the Louisiana Purchase, that I'm aware of. But like Rick said, there have been many local church parishes formed since then.
Also "native of" statements can be unreliable. For example, an 1805 baptism of James' sister Anne Neville shows their parents were "inhabitants of Bayou Boeuf" which is in today's Lafourche Parish. An 1826 marriage record of another sister Marie shows she was a "native of Alexandria" (Rapides Parish). Hints like this are a good place to start, but they can't be taken at face value and additional research is needed to verify.
Your best approach might be to research his parents and siblings, see if you can figure out where they lived, worked, baptized and raised their children. It's a tough period to research since censuses give so few details, but church records can help.
Many Catholic church records for this period are available in most libraries in south Louisiana, and in several major genealogical libraries scattered in other places. Much of the SWLR records are also indexed on FamilySearch, although they aren't always identified as such. If you don't have access, some of us may be able to help.
Best of luck with your search!