Louisiana Tech is the only established aviation program in Louisiana. LSU-Alexandria is trying to start an aviation program next fall (2022). The flight lessons will be given at the Alexandria airport but handled by a private ( part 141) flight school out of Lafayette.
As far as non-university flight schools: there are only 4 I would give any attention to. One in Shreveport/Bossier City. One in New Orleans. One in Lafayette. One in Hammond.
I worked for the flight school in Hammond. Part 61. Hands down a great place. No complaints. Well maintained aircraft, aged planes, no fancy glass cockpits but probably the most reasonable prices you’ll find in the country. I’ve never had direct contact with the school in New Orleans but plenty of first hand contact with former students and instructors and unfortunately never heard anything good about that place.
I can’t speak from experience about the other two schools in Bossier or Lafayette. However I’ve been to the airport/FBO of the school in Bossier and they have decent facilities and decent looking, equipped planes from both the website and seeing them in person (for whatever that’s worth which may not be a darn thing lol).