In our timeline, the French revolution was incredibly unstable. Power moved from the King to the National Assembly to the National Convention to the Committee of Public Safety to the Directory to the Consulate. It was only with Napoleon's coup that some sort of stable government came in, and then there was another 15 years of reasonable stability under the Restoration.
But how long can the 1789-1804 style upheaval continue, if we get rid of Napoleon? Is twenty or thirty years of a constantly shifting political setup possible? What would that mean for France? Could we see separatist movements and local warlords spring up?