The early 'unaccompanied' form refers, of course, to early balladeers singing at gatherings. These would be Acadian (French)
songs and ballads that they brought with them from Canada, songs picked up on the diaspora or after they arrived in Louisiana. Dances, jigs and reels, came with them.
As time passed, Spanish (from entrepreneurs in NO), English, Irish, Indian, Black both slave and free, and other influences blended in, along with music from German colonists. This mixture, which mostly took place in the 19th c, is known only from a few written mentions, so, as the article from Louisiana State University-Eunice notes, exactly how it got to be what it is, "is cloudy."

Good summary here: Contemporary Musicians and History