Haven't seen the Barbeau books, but the tune as notated in Le tour du monde en chansons, by Henriette Major and Patrice Dubuc, is more complex rhythmically than the tune rendered by Barry Taylor. Notably, it has a number of "Scottish snaps"; it sounds more characteristic of Scottish or Breton music than of other types of Acadian music. Sadly, the authors cited no source, but I assume it was copied from a collection like Barbeau's. Collectors and arrangers tend to simplify tunes for publication, particularly for kid's books, so this tune variant may be more reflective of actual oral practice (and probable origin) than the simpler version from Barry Taylor's uncited source.

One commenter (Barbeau?) observed that chestnut and pear trees were not native to Canada, so this song may have an old-world origin. Do chestnut and pear trees fare well in Canada? Is there an area of Canada--or France--where pears and chestnuts are primary crops? This could help narrow the path of transmission.

Even in English, there seems to be a rarity of theological riddle songs which cannot be traced to "False Knight". The closest French example that I've tripped across (a tale called "The little white angels and the little black devils") had the heaven-or-hell motif, but it involved serial questioners rather than serial riddles, and the children's fate was determined from their manner of reply, rather than by testing their theological knowledge or wit.

Of course, it's always possible that some Acadian cleric, familiar with the "False Knight" pattern, tossed together this ditty to inspire his young charges. In that case, would it be derivation, relation or separate origin?