I've met the militairy police in Paris as well. I was obviously not French (way too tall for the average French guy, can't talk the language and not wearing French-looking clothes). Intimidating bunch. One even flipped open his holster holding his pistol before talking to me in front of the subway. Couldn't understand a word he said and he wasn't really willing to talk English. Let me go on my way again. I kept thinking 'what are you going to do with a machine gun in a crowded subway? Shoot everybody?'