Please check out my earlier answer on this topic. There is always more to be said though, so feel free to ask if there's anything it does not cover. But in general I will mention that they did not send troops to send the Tsar (who had long since been toppled), but to restore an Eastern Front against the Germans.

This answer explains the motivations and gives an overview of the Allied Intervention, and also discusses the French participation more specifically.

This one looks specifically at America's role in the civil war.