What is the system of close combat taught in the Légion étrangère? How did it evolve during the history of the Légion?
CAC, the French name for Close Combat, was replaced by Technique d'Intervention Opérationnelle rapprochée (TIOR), apparently somewhere around 2002. This is taught throughout the branches of the French military.
Judging by what I can understand from École Interarmées des Sports Notice T.I.O.R., training appears to prohibit striking to the head, but authorizes strikes to the body and appendages. Also included in the training are escapes, gross locks, basic ground fighting, arrest procedures, sentinel takedowns (and basic counters to them), fighting with a baton, combat with a firearm, basic retention, knife fighting techniques, and operations techniques.
Like most modern military combatives, the training of the French Foreign Legion has its roots in W. E. Fairbairn's methods, and has adapted according to the specific needs. Specific branches may have more or less complete systems, or in depth training. Further, specific members may have access to more or less training than others, based on interest and availability near station.