How would history be different if Marquis de Lafayette stayed in France?

Answer 1

History has a lot of variables and the answers that I propose are just proposals, not definitive answers.

Individually (this is to say that only Lafayette didn't show, but the French Navy came under a different noble's command), Lafayette had a much more profound appreciation for what the American rebels were trying to achieve than most French did. He respected (although did not necessarily endorse) their right to political sovereignty and internal equality. This runs against the general French sentiment that they were joining the war to counter the rising strength of the British. (Help the enemy of my enemy sort of thing.) The application of this respect is that Lafayette was much more willing to cooperate with Washington and other rebel leaders than trying to order them around. The verbal antagonism between the Americans and a less respectful French leader would have led to a much longer war that would have claimed many more lives and would have made American success much less likely.

Communally (this is to say that the French did not join the American Revolution), the American Revolution would have been an abject failure. The fact that the French were able to break the British blockade alone allowed war supplies to come to America from Europe and partially arm the American Rebels. (This is aside from the additional naval and land-based operations in which the French took part.)