The French revolution didn't end with mob rule, it ended with Napoleon staging a coup on the french directory and seizing power. The french revolution lasted over a decade with many different governments taking power over its duration.

The only part that can be described as mob rule was the reign of terror that happened fairly early on during the first republic and half a decade before the end of the revolution. It was ended by the same revolutionary government it started under.

Revolutions in France also don't end with the French revolution, and eventually established the France that exists today

After Napoleon, the monarchs re-seized control until the July revolution in 1830, which resulted in a constitutional monarchy.

That government was overthrown by mass protests in the French revolution of 1848, which resulted in the creation of the second republic.

Napoleon III overthrew that government in 1852, and became emperor of the second French empire.

Because of Napoleons capture in the franco-Prussian war, the French national assembly established a new government, the 3rd republic in the rest of France, this new government surrendered to the Prussians in 1871, and elections were held in parts of France.

Workers revolted later that year, and established the Paris commune, it was defeated after a few months, but it did force the 3rd republic to enact reforms.

These reforms failed and Republicans took control of the 3rd republic, finally getting rid of the monarchy and selling off its assets, crowns, etc. to stop them from coming back.

The 3rd republic lasted until Nazis captured France in ww2