The following is a list of possible PODs in French history. Some have been explored on this board, others haven't. So this is basically a grab bag of suggestions, for anyone who might be interested.
A different treaty of Verdun, 843
Lothar's two brothers, whether by accident or wrongdoing, don't make it to adulthood. He inherits the whole of Charlemagne's empire.
The fire next time, 1307
King Philip and the Knights Templars strike a deal that enable the former to replenish his coffers without cracking down of the latter.
Perfidious Burgundy, 1435
Burgundy doesn't switch sides in the Hundred Years' War. With its ongoing support, England decisively defeats France.
The king’s life is worth a mass, 1610
As Ravaillac attempts to strike Henry IV with his dagger, a guard hurls himself before the king and takes the fatal blow. Henry IV is unharmed.
No help for the unruly mob, 1776
Louis XVI is advised against supporting the rebellious American colonists against their British overlords; instead France rebuilds its financial reserves, depleted during the Seven Years' War, and leaves the Americans to their fate.
The great escape, 1792
Louis XVI isn't identified at Varennes; he makes it to the border safely.
Alone in the night, 1799
Thanks to the betrayal of one of the conspirators, Napoleon's attempt to take over is thwarted at the last moment. Fleeing for his life, he eventually arrives in Louisiana.
Dawn of Pistonpunk, 1807
Nicéphore Niépce tinkers on with his prototype for an internal combustion engine instead of turning to experimentations with light-sensitive chemicals and inventing photography. He eventually develops a marketable automotive vehicle.
Master and apprentice, 1814
Exiled in Elba, Napoleon doesn't return to France. He sails to Venezuela and meets up with an admirer of his, one Simon Bolivar.
The baker’s bitter bread, 1889
General Boulanger successfully deposes the Third Republic and sets himself up as dictator.
A line in the sand, 1898
The Fashoda incident degenerates into a full-scale war between France and Britain.
A bottle in need of a cork, 1940
The French chiefs of staff realize the danger of a German breakthrough in the Ardennes, and prepare accordingly.
The other general, 1947
Leclerc doesn't die in a plane crash, but lives on to oversee the peaceful transition to independence in Indochina.
Fifty magic bullets, 1962
De Gaulle is killed when his motorcade is riddled with machine gun fire during an ambush by die-hard opponents of Algerian independence at Petit-Clamart.
Paris is burning, 1994
The Islamist terrorists who hijack Air France flight 8969 don't stop for refueling in Marseilles, but fly straight to Paris and carry on their plan, crashing the airliner into the Eiffel Tower.