You're right, it's Jimmy Breaux, and he's about as good as they come - an amazing accordionist.
Forget Beausoleil - get Jimmy's 3 cd's (if you can find them). I got mine from Floyd's in Ville Platte. They are all excellent, and I much prefer his work on them.
Yes it is Jimmy Breaux. I take lessons from him. He is as good a teacher as he is a player. Check out the Jimmy Breaux and friends album. Great songs and great playing.