Is there any immigration/security fast lane:
YES
Inbound:
Despite the SkyPriority sign, you need a TAV primeclass Fast Track Card (you can only get it at IST airport, so ask for one at AF check-in ciunter for your next flight
Outbound:
Same story. Despite the SkyPriority sign, you need to ask for a TAV card at check-in counter.
"Fast track has nothing to do with SkyPriority" said again and again the lady at Fast Track control, despite the SP sign and the fact that you can get a card at check-in as Skyteam Elite Plus
The AF supervisor did not know about the issue (and did not even know that there is a SkyPriority logo at the entry of the Fast Track).