Although it is quite possible to restore one of these clocks with the movement in place, it makes the task much more difficult. No clock-making skills are normally needed to remove a French movement from its marble case.
To remove the movement:
Remove the pendulum. You should do this anyway, as moving the clock with its pendulum fitted will almost certainly damage it.
The pendulum will have a small hook at the top. It either hangs on a thin strip of spring steel with a pin through it (the suspension) or it will hang on a piece of silk thread. Simply raise the pendulum enough to unhook it. Remove it from the clock. You may need to guide it through a slot in the arm that drives it.

The pendulum hanging on its suspension
French movements are usually held in place by being clamped to a back door or plate. If you open the back door you will see two screws going into two straps that are connected to the front of the circular movement. Before you undo them, remember that the movement might fall out when free to do so. If the clock is light, you can consider placing it face down on a cloth. If not, you will probably need someone to hold it for you.