Possibly but it makes prefect sense to arm occupation troops with left over weapons from the enemy. Having thousands of carbines or rifles and millions of rounds of ammo readily available is a prefect choice. Plus that allows the best newly made weapons to go straight to the front lines instead of troops in the rear or guarding less valuable sections away from the front lines. Being stationed in France in 1941 was alot safer then being sent to the Russian front in the early days of WWII.
But I have found alot of German Navy personal armed with French weapons though.