Today the patrol I saw in Paris' busiest train station were paratroopers wearing the distinctive red beret. If I remember their shoulder patches, they were from the 17th Regiment of the 11th Paratrooper Brigade. All three carrying their FAMAS assault rifles at low port arms. Each of them can send thirty 5.56 mm rounds downrange in a matter of seconds. They patrolled in a triangular formation with good separation and clearly were not a group to be messed with. They were not there to answer stupid tourist questions or to engage in idle chit chat. But if someone starts yelling "Allah Akbar" I imagine they would respond most effectively.
It's sorta like having your neighborhood patrolled by the 101st. There must be some sort of alert that nobody has told the public about.