Tom - All your suppositions are correct, except specialist platoon elements were indeed cavalry personnel; excepting the cyclists.
The remaining regiments I did not mention were stationed in Nord Afrika( Chasseurs de'afrigue, and Spahis).
Each metropolitan regiment was composed of a HQ element, and 3 squadrons, with a total strength of 32 officers, 650 men, and 671 horses.
To build a division required 3 brigades with 2 regiments per brigade, plue the attached elements previously mentioned.
Like the German composition, each divison was mixed with light and heavy elements. However, the attached Jaeger battalion gave the German divisions a decided advantage.
(I can provide combat examples if interested.)