The history of the Balfa brothers reads just like the story everybody in the folksy Sixties wanted to hear. Five brothers, sons of a sharecropper from Louisiana got together to play some authentic tunes for family meetings in the Forties, then started recording in 1951. Then in 1967 they started touring the folk festivals of the time, and were quite successful. This recording, made in the early Seventies, is proof of that.
Then in 1979 and 1980 the group lost two brothers in an accident and the wife of the band leader to disease. They were never the same after that. From the wiki it is not really clear if they still exist, but in some way they still might.
Cajun music is played by the French-Creole inhabitants around the Mississippi, but it is rooted in the ballads from a part of the old French colony to the very northeast of the continent. That place was called Acadia, and I suppose that’s where the name comes from: (a)cadian: someone living in Acadia. Pronounced a bit flatly you’ll get cajun.