Would the French revolution have happened if it weren't for the American Revolution?

Yes it would have in my opinion. The chief causes of the French Revolution are largely independent of the American Revolution. Although one can make the case that the impact of the American Revolution greatly catalyzed the onset of the French Revolution (via debt payment and the influence of liberalism).

The following were however the key drivers.

1. Economic collapse caused by poor productivity (often a function of severe winters) that was further exacerbated by grossly unfair taxes/tithes levied on the 3rd Estate. Push back by both the 1st and 2nd Estates against prudent compromise (recommended by several finance ministers - Necker, Turgot etc) further worsened the issue. Many of these economic problems were also compounded by France’s other wars (Seven Years war for example) and the Ancien Regime’s overextended imperialistic endeavors that were predicated on failed mercantilism.
2. Growing grass root Bourgeoisie agitation for political representation
3. The Influence of the Philosophers - Voltaire, Diderot, Rousseau, Montesquieu etc. that highlighted an unsustainable class structure that was on a collision course with both Enlightenment and later Romantic values.
4. Weak leadership by Louis XVI and an incompetent elite that operated around a bubble located at Versailles.