Edwin Edwards is not related to John Bel Edwards, who is the son of a former sheriff named Frank Edwards from Tangipahoa Parish. All of these Edwardses, however, are active Democrats.
Edwin has said they are
http://www.nola.com/politics/index.ssf/2015/09/edwin_edwards_on_trump_and_lou.html
“Edwin Edwards, a Democrat, says he’ll vote for John Bel Edwards. They’re distantly related, he said, but he also likes that John Bel Edwards was a critic of Gov. Bobby Jindal long before many others.”
I see no reason not to believe him and every reason not to believe John Bel saying “no relation”. In any case John Bel’s daddy Frank was a key Edwin Edwards crony and that’s even more damning than blood relation.