Perhaps the Reformation succeeds in the entire Germanic and Slavic societies, leaving only Romance societies as Catholic. It would create a binding institution needed for pan-Romanism to emerge.
If it were a Pan-Romanist people's movement with religion as a pretext, you've still got the issue of organising such a massive state with pre-1900 logistics, as well as coming up with some method to overcome any linguistic and cultural barriers, as well as sorting out the inevitably immense number of nationalists, regionalists et cetera. Unless it was an HRE-type state, where the head of state is the
de jure ruler only, it would be extremely hard. That's for if it were some kind of revolution like the French Revolution. As somehow I don't see the monarchs of Europe unanimously agree to hand over their thrones to one guy (or giving them up to a Republic).
In terms of a "New Rome" in stages, I see a French victory in War of the Spanish Succession, and the subsequently massive Franco-Spanish Union could then go on to conquer Wallonia and Italy for whatever reason (being the
de facto warlords of Western Europe, they could undoubtably manufacture a reason, following on from the religious clause, they could proclaim themselves the "Protector of all the Roman Christians"). Then they could proclaim a "New Roman Empire" or whatever. I doubt they would want anything to do with Romania though.
French and Italian Switzerland also aren't too Germanized, are they?
No, but they compromise about 30% (at the most) of Switzerland's population.