All right, all right, here I am !
Yes, they are part of the Army. Actually, the Troupes de Marine have the same TO&E than the rest of the French Army. The distinction is more a matter of tradition, and a training that involves amphibious operations.
The French Infantry Platoon is currently organized as followed :
1 Command Element : Platoon Leader, 2IC and RTO.
3 Squads : 8 men squad, with 2 three-men teams and 1 sharpshooter.
1 AT squad : 5 men squad with 2 ERYX ATGMs.
4 Vehicles : VBCI or VAB, 2 crewmen each.