Well, France stood little chance against Russia AFTER Napoleon got involved with the Spanish Ulcer and then made the monumentally stupid mistake of invading Russia in 1812 and losing half a million men to the Russian winter. Prior to that time, he pretty much kicked Russian butt whenever they got uppity.
Assuming he still does as he did in OTL in those two cases, I would agree with you. If some butterfly from the decision to dethrone the Hohenzollerns leads him not to make those particular decisions, then I think Nappy will continue to kick Russian butt whenever Tsar Alexander decides to come out and play.
Don't get taken in by the memoirs of the man himself! Boney initially had a hard day at Jena, and believed he had the majority of the Prussian Army in front of him. That he outnumbered the Prussians 3:2 and even 3:1 in some instances means he should have beat them even if they were in a prepared defensive position - or even a fortress! Davout was the hero of the day and performed what can only be described as miracles at the battle of Aurstadt. It was during that battle that Bernadotte let Davout down by marching away from the sound of the guns, coupled with his scheming during the consulate;it suprises me he did not get executed! So no Bernadotte for the Prussian throne!
Friedland and Eylau were no walk in the park for boney either! The losses from both accounted for a substantial number of men from both sides. Both desired the peace agreement that followed, especially Boney with his desire to complete the "Continental Blockade".
On that front, the mercantile nations of Europe were hurting really badly. Especially those on the North Sea coast and the Baltic - including Russia, all because of the Blockade. It is said that Holland, particullarly, suffered. On the Scheldt where many ship yards stood at the start of the Second Coallition, by the end of the Third Coalition only one stood of any significance. Britain, of course, benefitting hugely!
The point here is that Boney would follow OTL and endeavour to close Iberia to British trade. So the Spanish Ulcer would happen as in OTL.
Alexander was always going to size up to bonapart. After the latters flattery had worn off, alexanders aims re Poland and Germany would re-surface, not to mention the "right" of the hapsburgs to dominance in Middle Germany. Great Britain would not rest until a balance of power was restored, and in this, their greatest natural allies were the Russians and Austrians - even though bth hated GB with a passion! Prussia in some form or other will be negotiated, and then restored in the later unavoidable wars.