Serious question: When is the last time an open seat in rural Louisiana (not LA-1 and LA-2) did NOT switch?
LA-7 in 1996... if you ignore the fact that the incumbent had defected to the GOP before he retired. If you don't ignore that, then I think it's LA-4 in 1986.
There were several victims of the awful redistricting of 1992; Clyde Holloway (R), Jerry Huckaby (D). If you ignore those, the answer is, I think, Buddy Leach (D) in 1980. Beaten by Buddy Roemer (also D then). Leach had been mired in a vote-rigging scandal.
May have missed someone, somewhere.