How could you come up with a geographical division of metropolitan France between "traditional" republicans (so not commies or syndicalists or some other radical faction) and French monarchists of any stripe (including imperialists)?
Conservative and moderate republicans are the result of the collapse of monarchism in France, when it ceased to be a credible alternative between the 1850's and the 1880's. Orleanist bourgeois, for instance, massively joined up with the idea of a liberal republic at this point.
In a TL where monarchism or bonapartism is still a main political force, republicanism would be essentially a left-wing, a radical republicanism.
Is it because Paris is such an important power base that France doesn't divide nicely like German, Korea, etc. do?
Well, that's indeed a part of the problem : the centralization of french institutions, politics and decisions centers overall (not forgotting th heavy demigraphical and economical weight of the city) made it a place where most of things not only happen, but in an accelerated rate compared to other countries. It's why that while, contrary to the right-wing legend according whom provincial France isn't some sort of conservative paradise and Paris a political monstruosity deciding of everything, Paris is some sort of obvious political arena that no other city in France can hope rival.
There's other reasons, tough : french bourgeoisie, aristocract and overall middle-clas is particularily tied to the state apparatus in a way that no other western country was at this point. They really weren't prone to disband or weaken the french state just for shit and giggles, as their social sefety (and ideological alliegence) depended from it : it's why tentatives as Legitimsits in Vendée in 1832 backfired hilariously, without real support worth of mention. You need some serious reasons for a radical change, and when it's the case, well...most of higher classestend to agree all together.
For a geographical division in two states to happen, you'd need not just a serious crisis, but the disbandment of everything about higher classes and state apparatus in sight, something that would at best weary itself to the point of extinction trying to take over the other part.
Why no divided France scenarios except Brittany and Occitania and other distinctive cultural areas splitting off?
Because the knowledge on French politics in the XIXth tends to be, far too often, caricatural and growing out of baseless clichés?
Even a secession of Brittany in the XIXth makes very little sense in the context (and to be polite, I won't even dwell into an "Occitania" independence. Enough to say it's anachronical as ****) and the national and political idea at the time.