As the climate changes, olive trees have been pushing their way north in France, but it’s still only southern France and Corsica that produce olives and olive oil commercially.
Most olives are sold unpitted (if they are pitted they are olives piquées). You can also get cans of tasty olives from Spain, stuffed with anchovies (olives farcies aux anchois), pimentos, tuna or almonds.
Some French varieties are designated AOC/AOP...
Lucques: grown in the Aude and Hérault in Occitanie. Superb green or black table olive in a crescent shape. Also used for oil, but it’s difficult to extract
Images by Berthold Werner on Wikimedia Commons, chez loulou from France, Jean-Pol GRANDMONT, Véronique PAGNIER