France actually had a number of these light cavalry divisions. Most were formed during the mobilization when the peace-time cavalry divisions were broken up. There were also a number of spahi brigades (light North-African cavalry, entirely on horseback), an independent cavalry brigade (formerly belonging to one of the dissolved cavalry divisions), mounted recon groups and some mounted elements in the Foreign Legion. So France had way more cavalry than just one division.
My apologies. I only personally knew of the one home grown light division that fought in France itself. I wasn't counting auxiliary units in the French empire, any more than I was counting the many cavalry units in the Dominions in the British Empire.