WI: Napoleon marries into the Romanovs?

I was reading up on the Romanovs during the Napoleonic Wars and came across the fact that Napoleon originally wanted to marry first Ekaterina Romanova, Alexander's favorite sister, and when that fell through due to the Romanov's dislike of Napoleon he tried to marry her younger sister Anne. When Alexander pulled out of the marriage plans for Anne, Napoleon was angered and decided to marry Marie Louise instead. This was right after his divorce from Joséphine.

I am not sure how, but what if Napleon was able to get at least enough acceptance of the marriage to have it go through. Lets start with the marriage to Ekaterina. I am unsure of how much this change actually impacts the course of the war.

Would Russia start working with France with a marriage alliance in place, rather than the half-hearted efforts they attempted in OTL? With Russia on side, would anyone be able to challenge their shared dominance of the European continent? Does anyone know how this marriage might effect the dynamics of the Romanov family?
 
Napoleon might delay invading... at least until Alexander is dying and he comes to claim his rightful place as Tsar. ;)
Given that Alexander died in 1825 it would be a looong wait...

Napoleon should have allied with Russia (maybe supporting their efforts against the Ottomans?) and dismembered the Habsburg empire by leveraging the nationalities question.

A Romanov marriage would not be a surefire guarantee for a lasting alliance (just like the Habsburg match wasn't in otl) but it would probably give a better position to N. Whatever works to avoid the Russian disaster of 1812! Even if that means eventually throwing the Grand Duchy of Warsaw under the bus.
 
The thing is that Alexander really, really, really did not want to marry his sister to Napoleon, and went to quite transparently obvious lengths to avoid doing so. The only way this might happen that I can see is if Alexander and probably Constantine somehow die early, so that Nicholas is a child Tsar under some kind of regency. Although most of the senior nobility will still want to oppose Napoleon, Russia will lose if it gets involved without carefully preparing the way they did between 1807 and 1812, which is probably not going to happen without someone as able as Alexander on the throne. If Russia gets spanked trying to fight Napoleon a few times, as it did OTL without that preparation, then sacrificing the Tsar's sister to ensure a prolonged peace between Russia and France certainly becomes appealing.
 
The thing is that Alexander really, really, really did not want to marry his sister to Napoleon, and went to quite transparently obvious lengths to avoid doing so. The only way this might happen that I can see is if Alexander and probably Constantine somehow die early, so that Nicholas is a child Tsar under some kind of regency. Although most of the senior nobility will still want to oppose Napoleon, Russia will lose if it gets involved without carefully preparing the way they did between 1807 and 1812, which is probably not going to happen without someone as able as Alexander on the throne. If Russia gets spanked trying to fight Napoleon a few times, as it did OTL without that preparation, then sacrificing the Tsar's sister to ensure a prolonged peace between Russia and France certainly becomes appealing.

Actually, just to kill off Sasha/Marie Feodorovna might do it. Konstantin was pretty pro-Napoleon (much to the embarrassment of the rest of the Imperial family), and if he is Tsar then what he says goes, and no one's going to necessarily have the balls and say 'Your Imperial Majesty, the French are for fighting, not marrying' besides Dowager Marie Feodorovna (who was the main block against the matches OTL. She disliked Napoléon intensely, and basically persuaded Sasha at a family meeting that Ekaterina was much too good for Napoléon and Anna too young.
 
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