Finding old birth records in Louisiana can be a bit tricky.
Take my grandmother as an example. She was born along Bayou Boeuf in 1913. It was the same year the Model T started rolling off the assembly line in Detroit so the world was definitely changing and advancing. However, Louisiana wouldn’t start keeping statewide birth records for another five years.
Because she was Catholic, I found her baptism record, which made note of her birth date as well as the day she was baptized – no doubt screaming at the top of her lungs when the water hit her head. I have to imagine she was already a spitfire in the making.
Church records are a great resource if your ancestor was Catholic. Many of the records in south Louisiana have been published and can be found in local libraries.
Another thing to consider is whether your ancestor lived in New Orleans. For Louisiana records, New Orleans is always the great exception. Records there go further back than in any other city.
Family Search’s database of New Orleans birth records goes back to 1819. Search here.
Sadly, the images of the certificates themselves aren’t online. However, this is a good index that includes the parents’ names.
Happy searching!
louisianagenealogygirl 
I think the Diocese of Baton Rouge and the Diocese of New Orleans will send you digital images of the sacramental records if you order them. There is a processing fee, but it’s worth it!