What if there had continued to be an (anti)Pope in Avignon in defiance of the Pope in Rome?
And maybe while this pope is followed outside of France, in many ways this breakaway RCC is in reality a
Gallican Church.
The problem, of course, is that the "Pope" is, by definition, the Bishop of Rome. It's pretty hard to seriously claim that you are the "Bishop of Rome", when there is another guy claiming the same thing and who IS IN Rome.
The split in the Papacy was considered a huge scandal at the time, and people worked very hard to heal the split.
OTOH, the situation did endure for a considerable period of time, and I suppose it could have continued. It would certainly lead to the 'French pope' being essentially the head of a Gallican church, as you say.
I think that if the French actually get away with it, that others will, too. A Spanish pope, an HREGN pope. What happens when the Reformation hits will be very interesting. (Because the decreased authority and respect of the fractioned and factioned *RCC will have such a huge hit that even Hussites and Lollards might survive iTTL. A Reformation is surely guaranteed iTTL.)
Does the English church do its own pope or just go 'protestant'? lots of options. What do the Scandinavians do?