Americans and French had a few problems in common by the late 18th century. Both societies were very unequal, were unhappy with their respective taxation systems, and also with the Monarchy.
They also had in common a extended knowledge and appreciation of the Enlightenment philosophy. Then recent works on politics and economy were the basis for both movements.
The French used the American Declaration of Independence as a model for their Déclaration des droits de l'homme et du citoyen de 1789 (Declaration of the Rights of Man and the Citizen in 1789). They had observed closely the American revolution, since they supported it directly, and its possible that the American success proved it was possible to rebel and to win.
American independence and government also showed it was possible to build a new society based on Enlightenment ideals.