Think of the Emperor: his first objective is to destroy British economy by extending the Continental System. To enforce the latter, he has to control every European coast.
So, let's assume that's he think twice about the Russian Campaign and decide to use Smolensk as winter camp. He resumes the campaign in 1813 with fresh forces and marches towards St. Petersburg.
Russia is reduced to a secondary power: Poland regains its
1619 borders (maybe without the Cossacks gaining an own state), Crimea is made independent (Turkish-French protectorate), the Baltics are either annexed by the French Empire ("Les provinces baltes"), given to Poland or released as a French protectorate.
And yes, on the remaining Baltic shore, a puppet state could be set up. Just - how to name it, where is it's capital? I have the strong presumption that, at this point, St. Petersburg was actually more important than Novgorod. A more suitable name would be "Ingria" or "Ingermanland" with the capital St. Petersburg - or, "Kingdom of Novgorod", but with St. Petersburg as capital.
Expect it to be a French protectorate, either as military dicatorship with some aristocratic elements or thoroughly as a monarchy governed by a member of Bonaparte family.
Arkhangelsk as the other important Russian port may be attached to Novgorod too.