Russia was by no means invincible; 1805 and 1807 had clearly demonstrated that. They had also demonstrated that you had to push a Russian soldier over after you shot him, to let him know he was dead.
However, the biggest problem in Russia is simply one of scale. The distances are huge, and a French Napoleonic army would average 20-30 miles a day (the 54 miles Davout's corps did before Austerlitz was a one-off forced march that wouldn't be sustainable for more than one day).
Thus, I suggest that for Napoleon to win, he would have needed to split the campaign into two seasons. In 1812, he could advance to Smolensk, resting there for the winter or possibly pulling back to Mogilev or Vilna. As in OTL, he would hope but fail to bring the Russian army to a decisive battle.
With shorter supply lines, he would lose less to partisans (who would be less active anyway - they only really came out to play once the Retreat began) while in winter cantonments, and could maintain better contact with the rest of his Empire. In 1813, starting early in spring, he could strike at Moscow or St Petersburg. The latter actually makes more sense; it is the administrative centre while Moscow was the commercial and spiritual centre. It also has the advantage that his army can be resupplied by sea, if the navies of his allies in the Baltic can hold off the English navy (or, alternatively, if enough money can be found to buy the supplies from the neutral merchants who always found their way around a Royal Navy blockade).
It is likely that with either Moscow or St Petersburg threatened, the Russian commander would be ordered to stand and fight. It's why Borodino happened in OTL. Napoleon would have the advantage that his army would have been reinforced over the winter; in OTL, 85% of his losses were on the advance, not the Great Retreat. These losses were more drop-outs than death, due to illness and fatigue (it was very dry, hot and dusty as they advanced). With these losses replaced, Napoleon could have bought 250-300,000 men to a battle rather than the weakened 100,000 who were actually at Borodino. The Russians, too, would have been reinforced, but didn't have the resources of the whole of Europe to draw on as Napoleon did.
Following a defeat at the gates of St Petersburg (let's call it "The Battle of Gatchina" - quite a likely place for it to occur), Bruyere, Pajol, Chastel and Rozniecki could have driven the beaten Russian army north, into Finland. There, cut off from reinforcements, it could have been contained relatively easily. Not to mention that it might have been an irresistibly easy target for that great opportunist, Bernadotte.
With spring coming to St Petersburg around the end of March, which would be the start of campaigning, the decisive battle would have happened by about the beginning of June. In OTL, Napoleon crossed the Niemen on 24th June, fought Borodino on 8th September and occupied Moscow on 14th September, so it's a similar timescale. The difference is that ITTL, after the Battle of Gatchina Napoleon has another 3 months of campaigning before winter starts. He can use that time to move on Moscow, or to strike at Tula (the centre of Russian arms manufacturing), or to consolidate an occupied zone running from St Petersburg back to friendly Lithuania.
Assuming the Czar had any fight left in him after the loss of St Petersburg, he'd find it harder to organise new armies than in OTL, as he would have lost the administrative centre and key training facilities. I think it more likely that at this point, the Czar would open negotiations. Although complete French occupation of Russia would be unlikely, I can see Napoleon extracting a very heavy price. Finland could go to Sweden if Bernadotte had done anything at all to help. France could have set up proxy states in what is now Latvia & Estonia, possibly extending a zone of control right up to the gates of St Petersburg as a persistent threat if Russia got out of line in future. The Grand Duchy of Warsaw and Austria could both have picked up some land in the West of Russia. After four wars in a dozen years, Napoleon would have had little inclination to give Russia yet another chance, and the treaty would likely have looked like the one he gave Prussia with limitations to army size, massive reparations (in Prussia's case 100 million francs, from an annual post-treaty GDP of 69 million) and requisition of vast amounts of horseflesh.