-Napoleon tried to draw both the Ottoman Empire and Sweden into war, promising the former Romania and Crimea and the latter Finland. Obviously neither was willing to do so OTL, for good reason in both cases, but either would've drawn significant forces away from the main front. Sweden in particular could've presented a serious threat to Saint Petersburg.
-Had Napoleon brought back the Kingdom of Poland, it is likely that all of Russian Poland would've defected to him early in the war. He would've alienated Prussia and Austria, but it should've been clear from the beginning that their hearts weren't in this invasion. Another idea that hasn't been discussed as much (at least that I've seen) is for him to abolish serfdom. It doesn't really matter that he can't enforce it, the main benefit is that the entire Russian infantry was made up of conscripted serfs. Had they been fighting an enemy that wanted to make them free men, would they have fought as tenaciously against him?
-Alexander ruled out an offensive strategy very early once he realized he couldn't count on the support of the Poles (why he thought that was a possibility in the first place is beyond me), but even after it was clear the French would invade, Russian strategy wasn't set in stone. A significant group, led by Bagration, wanted to engage in a single decisive battle somewhere in Poland. This would've greatly eased the Grande Armee's supply issues, and a victory on the scale of Marengo or Austerlitz might've ended the war right there. Despite its numerous problems, I think the army Napoleon led into Russia was up to the task.
-Failing that, Napoleon should've stopped for the year at Vitebsk. It was a strong position, and would've allowed him months to reinforce and resupply his force. It isn't unreasonable that he wanted to carry on, it was late July when he captured the city and traditionally the campaign season would've had months left, but Napoleon should have read enough about previous invasions of Russia to know what was coming.
I don't know if the end result of all this is a Napoleon victory. He was clearly not at his best in this campaign, and his style of warfare was a poor match for Russian scorched earth tactics. But it certainly wouldn't hurt.
Rising to his feet, Napoleon issues new orders: Holy Mother Russia was being put off- permanently. Half of army group center was staying in Smolensk. Napoleon then asks for a map of The Ukraine- no, Ukraine please. The Kiev, errr.... Kyiv area in particular. If the Russians want their possessions of Poland, Belarus, Lithuania and Ukraine back, it was going to cost them.
What benefit could Kiev have possibly offered to the French? Napoleon needed a swift decisive victory to secure favorable terms, the entire genius of the Russian strategy was to draw Napoleon's army deeper and deeper into the countryside, denying him that opportunity and waiting for his army to die off. Kiev, and the Ukraine in general, was a backwater with no tactical or strategic value. Had Napoleon suddenly decided to swing his entire army hundreds of kilometers south, in the opposite direction of the Russian heartland, all to go conquer a provincial town of under 50,000, I'm sure Alexander and his generals wouldn't believe their luck.
The only useful area of modern-day Ukraine was Lvov, and the Duchy of Warsaw already controlled it. One of the few good decisions Napoleon made in the 1812 campaign was to ignore the southern theater entirely and let the Austrians and Russians pretend to fight there.
