Try switching to a different layout and see what happens in Final Cut Pro.
If yiou check the box in the system preferences (at the bottom of the same window you posted above) to "Afficher le menu de saisie dans la barre de menus",you can easily switch back and forth between different keyboard layouts. Just add one or two layouts.
I can switch between Portuguese, French, German, Italian, etc and Final Cut Pro recognizes them all (no need to evenquit FCP X, just reopen the Commands window and it shows the layout that I chose).
I can't see how using one French keyboard or another could make a difference.
What your post indicates is that FCP X is expecting a different layout than thne one on your keyboard. In that situation, typing A would be received as Q regardless of whether you were using your old or new keyboard.
For example, try switching to German - do you see QWERTZ in FCP X' commands window? Now switch back to French,, and reopen the commands window. What do you see?
If this does not nudge FCP X into recognizing the right layout, try deleting preferences. Hold down command and option while starting FCP X and confirm.
You'll have to reopen your library, and adjust any settings, but this won't affect any of your content.