Robert Finley may be the most unlikely success story in Louisiana music. A sharecropper’s son raised in a family of gospel singers in the small north Louisiana town of Winnsboro, he didn’t make music his primary occupation until he was sixty years old.

Finley performed all of his life, singing and playing guitar in church, nursing homes, schools and local venues. But if glaucoma had not rendered him legally blind, he’d likely still be a carpenter, plumber and electrician in Bernice, the sm...