Before Petain take control of the governement the french fleet operate with the RN ( hunting Graff spee, fighting in Norway, fritening the russian in finland)
After the surrendering and before opertion catapult most of the ship move to africa, mostly north africa. Some little units join the free french as the minelayer submarine Rubis. Some are interned in great britain.
Note that they didn't fight their intended target : the Italian as Italy go in war after the event.
During catapult the british seize the interned units and try to force the french fleet to dismantle. It turn to open fight at Mers el Kebir, but at some place like Alexandrie they go to an agrement.
Some of the seized ship was given to Muselier ( the free french admiral ) like the submarine cruiser Surcouf.
Thing become complicated for the french crew then. They are normaly allies, but the allied are f** brit who kill them and their wives haves german's tank near their houses.
The French don't attack allies position but fire on them when they are in position of threatening their territories. They try to act to prevent attack of their african territories.
The Battleship Jean Bart escape from Saint Nazaire ( near Nantes ) only 80% finished, without it's main engine operational to Casablanca. with his only turret she return fire to the USS Massachusetts who try to land free french forces.
Defending Dakar the Richelieu and was hit by a torpedo and stopped but can still repel the british WWI battleship, and the fre french fail to made senegal switch side.
After the invasion of the "free zone" and the French Africa thing became simpler for the french and numbers of ship join the free french.
But the main fleet, including survivors of Mers el Kebir was trapped at toulon with not enought time to launch engine when german sailor come in tanks. All ship but a few submarine was scuttled. The Italian navy manage to save some of these but all main unit was destroyed in a week long firework.
The battleship Richelieu go to New York to have a refit and was send to help the home fleet in norway, and then she go to the pacific in an RN task force.