French Revolution?

A little thought experiment I had in class the other day.  This is the problem with having a mind like mine that makes connections like this. 

The ultimate question became, did the French win the American Revolution?

In Modern Philosophy the professor was trying to pronounce Arnold Geulincx's name.  After being told he was wrong by a student who speaks French, he said "if it wasn't for us they'd be speaking German, so that gives me the right to say pronounce French however I want."  This was, of course, a joke, so don't get all upset about that.  But it lead me to think this: well if it wasn't for them we'd still be bowing to the Queen.  Which led me to this proposition: the French won the American Revolution.

But, my thought process went, French involvement, particularly monetarily, was a major impetus for King Louis XVI calling for more taxes.  (Pardon my quick and dirty history)  So he called for the Estates-General, which led to the French Revolution, which led to his departure, much death, Terror, the Republic, Napoleon, etc.  In many ways, France was worse off thanks to their Revolution.  So in that way, their involvement in the American Revolution led to their downfall.

I suppose it comes down to (at least) two questions.  Is a republic better than a monarchy?  Is secularism (a clear result of the French Revolution) better than Christianity?  Those are two big questions, of which I would answer "maybe" and "no way."  But depending on how you answer those two questions, you can answer my bigger question.  Did the French win the American Revolution?