I've always wondered if there's any connection between this song and the French character La Reynaudine, a hero of the Hugeonot (Protestant) rebellion against the Catholic monarchy in the 1500's. Apparently lots of "Robin Hood" type stories were told about La Reynaudine, and lots of Hugeonots came over to Britain to escape religious persecution.

It would explain the reference to Reynadine not being "brought up in Venus' train". Hugeonot protestants likened the Catholic emphasis on Mary to the worship of pagan goddesses like Venus. And he says in the song that he's on the run from the "Judge's men" - British judges don't go out looking for people, French judges do.

The song needn't be a translation of a French original, it may have originated in Britain after someone heard a "La Reynaudine" story from a Hugeonot refugee.

Just a thought. We'll probably never know.