Different relations can get different results to the same events and Napoleon can see Alexander as his equal or at least consent or be more willing to tolerate Russian trading with England if his son is to marry a Russian GrandDuchess or proxy.
If Napoleon lets Russia trade undisturbed with Britain, it's pretty much an admittance that the already dysfunctional continental system is completely defunct, and sends a clear signal that France isn't going to enforce it against anyone breaking it. British ships will soon be trading openly in every harbor in Europe.
And with no invasion of Russia, what does Napoleon do instead? Send a few hundred thousand more to die in Spain? The carefully crafted image of French forces as unbeatable that had been painted in the third and fourth coalitions is quickly being washed off, which was a reason Napoleon decided on war with Russia in the first place - he needed a shot of glory to remind the world that he was not to be trifled with.
And even if Napoleon won't attack Russia, there's no reason for Russia to not start pushing west sooner or later. The Duchy of Warsaw is still an insult to Russian dominion over Poland, a more harshly punished Austria means that at the very least Galicia is ripe for the taking by an expansionist Emperor, but why stop there and not go for Hungary as well? A continued French alliance means giving up the pretensions of protecting an old order by Russia, making it a-ok for them to redraw Europe to their own liking - hello East Prussia, hello mainland Sweden.
How close if France going to let Russia get before saying no? Their spheres of influence will meet sooner or later.
EDIT: Also Napoleon's son won't be at an age where he can actually be married until after the otl time for the Russian invasion, and it's easy to break an engagement if you want to go to war.