I’m glad you posted that, I actually just commented something similar myself.
Turns out the people I saw were actually soldiers based on the photos you posted, I thought they were gendarmes but their uniforms weren’t blue.
In Paris, there's city Metro cops, some of whom get to drive special lightning-fast little Peugot patrol cruisers. They will weave in and out of traffic going the wrong way and driving on the sidewalks if they want. I also saw big Yamaha 1300s motorcyles being used by the police more often that I saw patrol cruisers.
There's also the French Army patrolling around in the big tourist areas, and in the most sensitive places where hundreds of citizens might be a target for a terrorist attack, they use the Foreign Legion paratroopers. They roam around in squads of six or eight, with multiple squads in view.
And sometimes, the French Army stages military exercises in Paris. They just send in whole divisions for maneuvers.