It seems to have a problem identifying my keyboard, though (the keys
correspond to an AZERTY keyboard when I have a QWERTY). I do not
know if it is an ingame problem or a Crossover one.
You can test by running Notepad. From CrossOver's Programs menu, select Run Command. Select a bottle and type "notepad" as the command. Click Run. Does Notepad respect your keyboard layout properly?
If the keyboard input problem occurs in Notepad, can you tell me which keyboard layout you're using? This is shown in the Input Menu tab of the International pane of System Preferences. Is it an Apple-supplied layout or a third-party layout?