More than likely shootable.
I have an MAB model D. It is essentially the same internal design, but a trifle larger and was issued as a holster sidearm to French national law enforcement following the war. (The type was designed prior to the Second World War.) The model C was a bit smaller and used as a concealment arm. If Clouseau carried a gun, it was likely an MAB model C. The caliber is .32 ACP (or 7.65 Browning, if preferred) and 'modern' ammo is essentially the same as 'period' ammo.
With all that, I have test fired my MAB model D. For all the jokes about French guns and .32 ACP caliber, it shoots well to the sights, has a manageable trigger (for an issue pistol) and pushes the .32 ACP projectile a bit fast than any of the other .32 ACP pistols I have.
To the original poster, I would not be afraid to shoot the pistol - ABSENT any cracks or obvious defects. If one desires to inspect the fired brass - something I do with 'new to me' guns - bring a spotter; the brass gets flung hither and yon. As always, safety glasses, hearing protection and proper examination is indicated.