The French unit structure is moderately similar to the German, with the largest difference being that the German kompanie has three Zugs, while the French Company has four Sections.
There's an additional complication in how Henri's unit is put together at the regimental level. Each active duty French regiment was quartered at a particular depot. Henri's regiment is the 104th, based in Paris. However, when the reserves were called up, they were placed in a separate, reserve regiment whose number was that of the parent regiment plus 200. Thus, Henri is part of the 304th Reserve Infantry Regiment. The battalions and companies of this reserve regiment continue the sequential numbering of the parent regiment. Thus, Henri commands the 22nd Company, which is in the VI Battalion.
In the novel, I've had the VI Battalion attached to the 104th in order to help make up casualties that the 104th suffered during fighting in the Ardennes, prior to being pulled back to Paris via train and then dispatched to the Battle of the Marne using a fleet of Paris taxis.