The first commercially-successful recording of Cajun music is generally acknowledged to be “Allons a Lafayette,” performed by Joe Falcon (accordion) and Cleoma Breaux (guitar). She would later marry falcon and be known as Cleoma Falcon. The blog The Singing Bones has a well-written appreciation of Cleoma. Her brothers Amédée, Clifford and Ophy recorded as the Breaux Frères for Columbia Records after Cleoma married Falcon.
The author links to a download of Cleoma Breaux songs. I do not recommend it. The hosting site is full of popup advertising and throttles bandwidth to a trickle for a free download. I’d like to have seen the list of recordings in the compilation.