The US independance was completely inspired by the "Lumières" (the philosophical movement of the Enlighteners), which originated in France and led to the French revolution as well as the emergence of true democracy accross Europe. So even if the US was already independant by the time the French Revolution happened, this is only because it was way more complicated to achieve the latter. But let's not be mistaken about its origins.
There was a lot of inspiration the other way too, though.
Here are two little instances I came across recently where the french copied their rhetoric and symbolism from America:
In 1787 Thomas Jefferson said, "The tree of liberty must be refreshed from time to time with the blood of patriots and tyrants". Then in 1793 Bertrand Barère, in an influential speech to the national assembly advocating execution of the king, repeated "The tree of liberty grows only when watered by the blood of tyrants" . In French sources the quote is often (incorrectly) attributed to Barère only.
Similarly, during the American revolution, Americans raised symbolic "liberty poles" in their towns. Directly inspired by this, during the french revolution most cities raised and decorated "Trees of Liberty" in their central squares. King Louis even stooped to visiting and honoring the one in Paris to appease revolutionaries (it didn't help).
(The French took the idea of "watering the tree of liberty with the blood of tyrants" quite literally).
Let's not make nonsensical statements like US independence was completely inspired by the Lumières then.
Most notably, US independence was also inspired by the Glorious Revolution in England (the American Bill of Rights is even based on the English Bill of Rights), about a century earlier.
"The Lumières (literally in English: Enlighteners) was a cultural, philosophical, literary and intellectual movement of the second half of the 18th century"
