Catholic England is harder in my opinion. I can't see the mercantile classes that held the power in England to be willing to submit to the Pope's edicts longer term.
No, you are confused. Charles Inglis was ordained regularly and officially as the CofE bishop for Nova Scotia.Not till C19 (by which time it was not British North America of course) . The question of Anglican bishops is BNA in pre revolutionary C18 was a very vexed one .
The first bishop in BNA of the CoE was in 1787, though Inglis was consecrated by the Episcopalian Church Of Scotland in 1784 .
The first primate of Canada was not until 1893 however.
This would probably be different if England were Papist.
Perhaps it be like Korea, "WE are the real Korea" even though neither side can really claim any control over the other.I'm sure you could do something with a surviving anti-pope in Avignon. Although you'd have to bridge the rather large gap between "WE are the real Catholics" and the antipopes recognizing themselves as a religiously separate organization from the Roman Church.
How Catholic may your Church of France be ? Calvinist or 'Church of Rome sans the Pope' are your extremes (the latter being Henry VIIIs original Church of England.