Actually, the roads had been better than during the War of the 4th Coalition about which Napoleon said that for Poland the God invented the 5th element, the dirt. The offensive stage of the campaign of 1812 happened during the summer/early fall which were mostly dry and, until Napoleon failed to prevent junction of the Russian armies, it was happening on a reasonably wide front with Davout acting as pretty much independent army commander trying to cut off Bagration’s 2nd Army (task in which he was almost successful but “almost” does not co7nt). Even at Smolensk there were attempts to cut off the Russian army (task simplified by the quarrel between commanders of the 1st and 2nd Russian armies which almost made it successful). Only when they failed, a straightforward pursuit by the Smolensk Road started but by that time summer was dry and a road wide enough to allow marching by few parallel columns. However, by that time the campaign was already strategically lost and even victorious major battle would not save it.
At Borodino, the Russian position was allowing the French maneuvers against both flanks so the choice of the OTL plan was strictly Nappy’s decision. With the campaign going nowhere, he expected that a major victory would provide enough of a psychological pressure to force Alexander to start peace talks and manauvers could result in a further Russian withdrawal without a battle.
As for the supplies and logistics in general, this campaign was a classic illustration of the shortcomings of the system. There were adequate food supplies carried with the army in the beginning but the horses started suffering from forage shortages soon enough and cavalry troops demonstrated a complete incompetence in taking care of them. Then, the army did not have a well-organized supply service in general relying on the looting activities of the small detachments. Napoleon ordered organization of few big magazines along the route but they were not guarded properly and on the way back had been mostly looted by the disorganized troops. Getting food from the nearby area was done by a traditional looting with the occasional attempts to pay by the counterfeit paper money to which Russian peasants were not accustomed. As was commented by one of the Russian contemporaries, if the French were paying in gold and silver, they’d have little problems with getting food and forage. When the retreat started, there was enough food available in Moscow and nearby region but Napoleon did not give the explicit orders, Bertier did not perform his duty as a chief of staff and, with the exception of Davout, the corps commanders did not care. Army went out of Moscow overburdened by the loot, short on supplies and only horses of Naploeon’s Household got proper winter horseshoes.
From Calabria to Spain to Russia, to say nothing of half of Massena's career, it seems like an overdependence on looting was a persistent weakness of the French army in this period. Wonder if anyone else was really much better, though. The British were spoiled by their navy and fighting in friendly territory on the Peninsula.