I knew of one place. I don’t think it’s still open. It was called Crawfish City of Texas - a metal building plopped down on a corner, with a wooden deck in front for the order window and on one side with picnic tables and a wooden ramp for a drive-thru window. They sold raw and cooked crab and crawfish. There were 3 food trucks on the lot, too, and when they weren’t open, the crawfish place offered some of their menus. All featured Louisiana specialties and I guessed all were run by Katrina refugees. The trailer offering fried catfish, boudin and gumbo was really good. I never bought any of the crawfish.
Most Cajun restaurants are smallish but sit-down rather than counter-service/drive thru affairs and wouldn’t qualify as fast food.
Another thing we have a depressing lack of is drive-thru boudin huts! I found one on the NE side in what was probably originally a Jack in the Box (the very early, boxy buildings). Actually they had a one-page menu of Cajun/Soul Food dishes but they called it a Boudin Hut.
Some gas stations with offerings like hot dogs, fried chicken, microwavable burritos, packaged sandwiches, etc., will offer boudin, too.