I saw a single reference to a French outlaw ("la Renaudie"), alongside references to an Italian outlaw ("Rinaldo Rinaldini") and an English outlaw ("Reynoldin"). If I was going to follow up any of those it would be the last one.

On the point about the (lost) progenitor song, all I would say is that I wouldn't expect any song that predated "The mountains high" to be closer to "Reynardine" than it was to "The mountains high". Otherwise you'd have to argue that the oral tradition turned a song seething with unavowed magic and repressed sexuality into a common-or-garden "maiden's warning" number, and that Bert Lloyd saw the diamond in the rough and restored it to its former glory. It's all a bit 'green man' for me (Sedayne, are you there?).