Actually, the French supporting America convinced the King of France to enter the American war as sort of a sccond front. The effort bankrupt France, led to the revolution and the king losing his head
A very significant factor in the start of the French Revolution was food shortages caused by bad growing conditions. The Laki Fissure in Iceland had been throwing off sulfur and other noxious materials for quite a few months in, I believe, 1783 which caused starvation in Iceland killing most of the cattle and about 10,000 Icelanders, but also widespread crop problems in various parts of Europe for several years.
The British were also busy at the time keeping control of India which was considered far more important economically than The Colonies. So the economic drain of conducting the war here was also a factor for them.