were the french soldiers even armed?
They also have a national police force (Gendarmerie nationale) that is sort of a border patrol. You see them at subway stations, train stations, airports, highways, etc.
At the national landmark sites like the Eiffel Tower or the Arch De Triomph, those are usually more elite units like paratroopers or sometimes even the Foreign Legion if there have been verifiable public threats.
There's some pictures here:
Probably. When I was in Paris two years ago I saw two gendarmes patrolling an area where a lot of African immigrants scam tourists.
They looked like military personnel, with berets, fatigues and FAMAS rifles at their sides. Tough looking dudes.
National Police carry pistols too, that’s one thing they have over the Brits.