Then France goes bankrupt and, as a result, the monarchy is abolished, given over to an Emperor, unabolished, abolished again, unabolished, abolished, given to the former Emperor's idiot nephew, and finally finding an actual democracy between the couch cushions.
19th century France was a trip, and intervening in the American Revolution sorta set it all off.
American Revolution was the kickoff, but there were a lot of other things building up for a long time, and they'd have found another way of going bankrupt fighting the English sooner or later.