Deep air was quite normal in CMAS courses in the past century.
My recreational diver and instructor certifications are to max depth 50 meters, with deco on back gas (no accelerated deco with high oxygen mixtures).
In some countries the local CMAS federation was allowing to even larger depth, as the deco limit was PPO2 <= 1.6 bars, which is something as 54 meters.
Definitely deco diving is considered normal and fully recreational in the Mediterranean, as most nice dives are in the range of 40 to 60 meters.
We consider "tech" the usage of different mixtures along the dive and the deco profile, and of rebreathers operating with variable gas composition.
My recreational certification includes pure oxygen CC rebreathers down to 10 meters (ppO2=2 bars).
Things seem to have been changed in this century. Most national federations adhering to CMAS now have a recreational depth limit of just 42m. I have just checked on the FIPSAS web site (Italian federation adhering to CMAS).
Deco procedures require an "advanced" certification (which is somewhat between "full rec" and "technical").
Advanced Nitrox allows for accelerated deco with highly oxygenated mixtures, up to 100% oxygen.
Coming to the OP: also in France many different organizations are active.
If you are interested in technical diving, perhaps it is better to start with an organization specialised in technical diving, not with one specialised in recreational diving, which just provides some "advanced" course as "intro to tech".
If instead you are OK with current "recreational" limit of 42 meters and deco with back gas, any organization adhering to CMAS will provide this easily. I still suggest the "advanced Nitrox" additional certification, it can be useful to use high oxygen mixtures in some diving profiles.
Forget about "deep air" down to 60m, this is in some way a relic of the past, it will be very difficult to find an old instructor still teaching this, which is considered too much dangerous nowadays.
I did dive that way in the eighties, I will never do that again!