Would a civil war resulting in a stalemate, and thus a de facto partition count? The third state could be an independent Corsica, or something, that capitalised on the civil war.
(At the time of this writing there are seven active separatist movements (French Basque Country, Brittany, French Catalonia-Roussillon, Corsica, Savoy, Provence, Occitania) and seven active autonomist movements (Alsace, Brittany, Corsica, Nice, Normandy, Savoy & Occitania) within Metropolitan France.) Granted, it is highly unlikely (barring perhaps whatever happens to Catalonia, but that's a topic for another day) that either of these will gain independence in the modern day.
I'm not sure how you are defining "active" but these movements for the most part aren't taken that seriously. Corsica has the strongest nationalist movement but even then there is a lot of doubt that it could be a viable state, having only 300 000 inhabitants.
There are regular calls for more decentralization of the French state in favor of the regions, though that's been the case forever.
What would cause France to lose Corsica to Sardinia/Italy any time after 1813?
I'm not sure how you are defining "active" but these movements for the most part aren't taken that seriously. Corsica has the strongest nationalist movement but even then there is a lot of doubt that it could be a viable state, having only 300 000 inhabitants.
There are regular calls for more decentralization of the French state in favor of the regions, though that's been the case forever.
Malta is an independent country but has less than 420,000 people. Independent Corsica would be heavily reliant on nearby countries but definitely could be viable.
But there are key differences. Malta is very small (316 sq km), almost a city-state. Singapore and Hong Kong are larger.
Corsica has a small population covering a much larger area (8680 km2) to defend and administer. It's much more costly to provide services to everyone on the island when they are spread out so much more.
Les Voyages Fantastiques et Miserables?Hugonauts
If we even see a French partition in this timeline, the newly-independent states I see (based on ethnicity) are: Corsica, Brittany, Basque, Alsace, Burgundy, Occitania and Savoy with a rump France as well.
There isn't really much of an Occitan identity to start with, though. You could have an independent Gascony (speaking Gascon), an independent Duchy of Toulouse (speaking Languedocien), or an independent Provence (speaking Provençal), etc.
Maybe if you have an independent Aquitaine it could have an official language that is derived from an Occitan dialect.
Lorraine- an independent duchy up until the mid 1700s, could potentially be made independent as a consequence of the Napoleonic Wars... would be very difficult, however, maybe an alt-Napoleon or an early defeat of the Revolution
Brittany- nominally independent into the 16th century, could be made into an independent kingdom by a stronger England
Provence- strong regional autonomy, several foreign claimants, integrated late with the demise of the Anjou
Gascony- hotbed of the Hugonauts, likely requires either an English victory or a major change
But in general, go backwards from when the provinces were annexed:
Nice/Savoy- 1866, easily could be part of ATL Italy/Sardinia Piedmont
Corsica- See Carp's timeline. Alternately I think this is just about the only territory that could plausibly be separated from France at OTL Vienna, especially given the Napoleonic connection
Lorraine- an independent duchy up until the mid 1700s, could potentially be made independent as a consequence of the Napoleonic Wars... would be very difficult, however, maybe an alt-Napoleon or an early defeat of the Revolution
Brittany- nominally independent into the 16th century, could be made into an independent kingdom by a stronger England
Provence- strong regional autonomy, several foreign claimants, integrated late with the demise of the Anjou
Gascony- hotbed of the Hugonauts, likely requires either an English victory or a major change