No worries, if the allusions continue further, France will cleanse itself from it's nationalist past after WW2 and become the next economic juggernaut of Europe, and leading an economic union of European nations
I don't think France can cleanse it that easy ITTL. Up to this point, much of French history since the Revolution has largely consisted of alternating between monarchy (sometimes benign, more often reactionary) and republic (with the excesses of the First Republic already known by now and the Second and Third Republics ending up as transitional periods for Bonapartists), with loads of nationalist currents bound up in those two, whether you want a resurrection of the ancien régime or a more progressive republic (that devolves into utter chaos by the bickering of politicians). France is essentially the birthplace of modern nationalism, so while it can't really cleanse it, it has to come to terms with its legacy and thus make a final choice - who and what do you want to be in the future, et pourquoi?
The key to all this, IMO (which would be coming out of left field), is going to be across the Atlantic in Québec. While France agonizes over what it wants to be, Québec does not have that sort of luxury since because of the Conquest (as well as ethnically cleansing the Maritimes of any French presence to make room for British settlers), French-Canadians bypassed the French Revolution completely (and indeed many French-Canadians were horrified by events going on in France - particularly when the French executed their king, which was unthinkable). Therefore, the ancien régime from the colonial era lasts MUCH longer than it ever did in France and adapted to living under first British colonialism and later an autonomous Canada and then the situation we've had in the past couple of updates, with an independent Québec surrounded by French-Canadian communities in the US under varying degrees of pressure to assimilate and resisting it along the way as much as it could. So what Charles Maurras, Action Française, Maréchal Pétain, and others basically dreamed about IOTL, as well as their counterparts ITTL, was already living reality (more or less) across the Atlantic. How French-Canadians themselves reacted to this status quo varies considerably between whether one is a nationalist or a common person, on one hand, and if one was a conservative or a liberal politically, considering their very flexible attitude towards the Church. (There's a reason why among French-Canadians the strongest profanity one can utter is actually religious in origin, and even then it's tossed around quite a lot - unlike the situation in Europe, where the strongest profanity is based on bodily functions, prostitution, and the like.) If and when MacArthur does gain control in Québec, it's more than likely that the Government in Québec will probably have to go into exile - probably to the old colonizer, the UK. It's then, when you have the Québec Government trying to make contact with its citizens, that two very different worldviews - the French worldview and the Québécois/French-Canadian worldview - come face to face for the first time since the 18th century, and the initial first contact ain't going to be pretty. There's a reason that for a very long time all French people were referred to in French-Canadian nationalist lore as "the evil French" (better known in the original idiom as "les maudits Français"), for selling les Canadiens down the river in exchange for making a quick piastre, abandoning them to their fate. This sense of abandonment animates the French-Canadian nationalist consciousness to varying degrees and is a main driver for
la survivance - basically, if France can't help us survive in North America, then we'll have to make do on our own to ensure the French language and culture continues to exist in the face of Anglo-American pressure. It evens shows up in popular representation of the
Aurore Gagnon case, which was the event of the century in 1920s Québec (more so than the Scopes monkey trial will ever be); I'll leave it to you to figure out the allegorical representations of that case. This, too, was at the latter end of the period of ultramontane French-Canadian nationalism, with its conservative, rural, and messianic overtones, which would seem at first glance to dovetail quite nicely with Action Française - oups, le Parti patriotique national (and I'm sure I got the gender wrong on one of those adjectives) - and their ilk.
However, that is when the two worldviews diverge. Since Britain is probably going to be chock full of French exiles - the purged - they are probably going to be scratching their heads over why Québec (or at least its Government) would cling onto such a thing. After all, since 1763, Canada has not really registered onto the French consciousness, and meeting actual Canadians (let alone Québécois/es - actual
Canadians) they'd probably see them as being too naïve, childish, easy to take advantage of, "les paysans" (with all the negative connotations that that brings up), and the like. One could see that as a reflection of the French psyche itself, which is pessimistic, cynical, stand-offish, not really being trustworthy of one's neighbours, chauvinistic, etc. etc. All qualities which French-Canadians tend to disapprove, instead going for the warm, community and family-oriented nature, politeness, openness and tolerance, mutual consensus, etc. etc. that defines how French-Canadians view the world. It's something that would not be noticed by French-Canadians and French people themselves - indeed, even as the radio of both the Government in Exile and the Québec Resistance have their entertainment programming filled with characters one can easily relate to, like (for example)
Séraphin Poudrier (in French only), for example, those same radio signals beamed back to North America from Britain would also be heard in France as well due to proximity. It's the difference of being in the majority (France) versus being in the minority (French Canada). One shouldn't forget, too, that the 1920s and 1930s is when Québec starts to change, becoming more industralized and modernizing at the same rate as other Canadian provinces IOTL and other US states ITTL, which French-Canadian nationalists tried and failed to prevent. So, therefore, when French people and French-Canadians come into contact, all they'll probably see are mirror images of each other.
This Franco-Canadian encounter will probably have lots of consequences in the long run. In North America itself, questions have already been raised as to the future of ultramontane French-Canadian nationalism and its obsession with survival in Québec, but when faced with the contradictions between a significant portion of the nationalists favouring someone like a MacArthur or a Napoléon V (or, IOTL, Mussolini, Salazar, Franco, Horthy, - the list goes on) in power - especially with a more right-wing France which makes the country "one we could love again" (even though IOTL in order to make that bit work it had to suppress certain details about Pétain, such as his world-class skirt-chasing abilities and his divorce) - when the Resistance and the common people see otherwise? That will definitely lead to consequences in the long run which the Government in Exile, once back on Québécois shores, cannot ignore. It couldn't ignore them anyway, seeing as it was close enough to the action. On the other hand, being exposed to French-Canadian media (despite any and all prohibitions on such broadcasts Paris might impose) and, for the exiles, interacting with actual French-Canadians, that's going to raise a lot of questions within France. For sure, French-Canadians definitely are not French people. But this was what France could have been had the Revolution not occurred, and while many elements of French-Canadian society would definitely raise a lot of questions, the strong community-oriented identity and the pragmatism French-Canadians deploy in their daily lives, as well as the nation treating each other as one large family no matter what political differences one would have (because after all you and I are probably either related somehow) would definitely impress some among the French as something their nation lacks with its cynicism and political polarization. A definite humbling experience for both France and for Québec. An economic juggernaut France might not be, but a France where it actually for once
learns something from one of its former colonies? That would be mighty impressive indeed.
At least that's how I'd see things.