It didn't have all that much to do with the French Revolution. When you talk about revolutions inspiring others, there's usually a lot less than twenty years between them, like the Arab Spring, the 1848 revolutions, the rebellions in 1968, or the revolutionary movements after WWI.

It also doesn't seem to have been on their minds much. I've read a lot of texts written at the time, and it just doesn't come up that often, at least not often enough to say that it was a major influence. They were much more drawn to the murder of Caesar, and the founding of the Roman republic, both of which are constantly referenced in speeches and articles. Their main philosophical inspirations were French, and older than the American Revolution, like Rousseau and Montesquieu.

It did have an influence on the French Revolution, though. The French state never really recovered from the expense of supporting the Americans. The debt, and the inability of the old regime to pay it, was one of the reasons for the beginning of the revolution. And several influential individuals had become famous for supporting the Americans, like Lafayette, and Thomas Paine. The French revolutionaries were certainly fans.