It doesn't sound like you're looking for any old-school adventure games, but the Gabriel Knight series is set in New Orleans, and provides some of the best southern bayou atmosphere I've ever played. It has all the heavy accents, Voodoo shops, and mosquito buzzin' you could want. Whenever I play Gabriel Knight, I can practically feel the swampy humidity in the air.
Speaking of Voodoo: it's not set in the bayou, but Risen 2 is about a pirate who can use Voodoo magic. It's not necessarily a good game, but if you like old Haitian Voodoo, that's an option I guess. --- . . . methodical, exacting, and worst of all, patient.