I am a Frenchman, right now a lawyer, but before that a specialist of French legal history.
It's not really my main "activity" anymore, but I'd wager that the only people who have an understanding better than mine of French legal history from the 15th century onward, especially since the French Revolution, are active historian doing research, so I don't come here to be explained the actual history of the French Revolution. I welcome information on the American war of Independance though, I know a little about it but not much.
And well, I have been working between France and the US for a few years now and I discovered something that I didn't know: in American popular culture, most people seem to actively believe that the French Revolution was a result of the American one, that somehow the French discovered liberty and freedom with the American war of Independance, and that they wanted to bring it back home.
That's so farfetched I wouldn't know where to begin to explain why it is wrong.
So where does that come from ? Who, or what, popularized the idea that the French Revolution was somehow a copycat of the American one ?
I think you're rather underestimating the impact of the American Revolution on the French. Mirabeau drafted a bill of rights in 1788 that was largely influenced by the 1776 Virginian constitution, for instance; the National Assembly debated the American constitution at length; and in general many French thinkers, among them J. J. Mounier, thought that America was the best model for French government. At an intellectual level, at least, the American model was very important, even if we can't say that the American Revolution caused the French.
As for the historiographical question, the simple answer is that the idea that the American Revolution caused the French goes all the way back to 1789 itself. Even prior to the fall of the Bastille, Thomas Jefferson wrote in January 1789 that "the American war seems first to have awakened the thinking part of this nation [France] in general from the sleep of despotism in which they were sunk". Though federalists like John Adams came to draw a sharp distinction between the American and French revolutionary experiences, the Jeffersonian supporters of the French Revolution in America tended to carry on conflating the two.
This was also true to some degree on the French side: already in 1786 Condorcet was arguing in "De l'influence de la Révolution d'Amérique sur l'Europe" that "the American Revolution is soon to extend to Europe", and during the Revolution itself he drew on the political ideas of the US constitution and continued to see the American experience as decisively important.
Aside from the pure question of causality, I should also add that there is a more overarching, and perhaps easier to accept, idea that the American Revolution and the French were inextricably linked. The French and American historians Jacques Godechot and R.R. Palmer gained some fame for arguing that the two revolutions should be viewed along with other disorders in Europe as a single movement called the "Atlantic Revolution", and while that specific view isn't so common nowadays the general idea that the two can't simply be dissociated and viewed purely in their national contexts is widely accepted.