Consider Naples: Josheph would have to give up with it in order to make peace.
Well, actually only Russia, Britain and (i think) Portugal are at war with France in this moment, but Austria will probably join. Russia would negotiate, but outright support to France is unlikely, unless they hope to grab something from the Austrians. It wouldn't be that wise, however: that's upsetting the balance, and till this very moment Russia had been fighting exactly to stop france doing so. Alexander did care of that enough to make Prussia survive at Tilsit.
The big game for the Russians now, if France could be handled reasonably, is the war with the Turks. Constantine held that name because Catherine the great was dreaming about him as the would-be Emperor of a revived Byzantine Empire. In Constantinople, of course.
In OTL Tilsit Napoleon forced Alexander to retreat from the Balkans, where the Russians were occupying most on Danubian principalities and were going to help the Serbs in their uprising. Russia also held Kotor in present day Montenegro.
Joseph could not even dream of asking that, or anything else indeed. He will leave the Turks alone (not that Napoleon really cared about them so much actually) and will make the quickiest possible peace with the Tsar, even more so with Austria jumping at his throat and half the German principalities likely in rebellion.
By around 1810-12 you may probably have
a) a treaty signed somewhere in Bulgaria securing independence for Serbia and probably Greece and giving Russia a large chunk of Eastern Balkans and Turkish Armenia, at least everything north the Danube,
OR
b) the Russians pushing even more, so triggering a war with Austria and Britain (France may be on Russian side). That's the "Constatine proves himself an idiot" case. Well, he may think "Austria is exausted out of previous wars, Britain has France to deal with, let's talk with the Americans and try". He's even a little hope of winning that war and being crowned in Constanople, IF the Anglo-American is not butterflied away AND it gets more bitter than OTL. Hell, a very little hope in any case.