Possibility 1)
https://en.wikipedia.org/wiki/Malet_coup_of_1812
His dynasty is lost, and Fouché, Talleyrand and some ambitious general having staged the coup will become the rulers of France.
Possibility 2)
Loyal supporters of Napoleon, like Cambacérès, the Marie-Louise, Joséphine, and Napoleon's brothers think that Nappy is alive and are able to convince the soldier that there is conspiracy against the Empereur. Even if later on is becomes clear that he is really dead, the supporters of a coup d'état are compromised and a regency for Napoleon II is formed.
In both cases, I see the French government trying to get the soldiers out of Russia as quick as possible and then to seek peace with Europe. France will likely maintain its borders of 1812 and the vassal states in Germany and Italy. Everything else, especially Poland and Illyria, will have to be returned to Austria and Russia to reach a peace agreement.