I got this framerate problems on 2 differents occasions:
1- When I first purchased, installed then started AZS from Steam.
Shutting down, then restarting my Computer solved the problem. Everything was fine and smooth.
2- Each time I play a game (Test Drive Unlimited 2) using my XBox 360 PC controller, then later (without rebooting my computer) start an AZS game.
AZS start with the framerate problem. But to solve this, I just need to turn on my Xbox controller, making sure AZS is working normally, then I can turn off (removing battries) the controller and I can play AZS without problems.
I'm no expert, but it seems that as soon as I use my Xbox controller, it somehow 'corrupt' my Computer and/or Steam, and this corruption make AZS unplayable, unless I start the controller.
I'll try playing a few other games using the Xbox controller, to see if I get the same result than playing TDU2 then AZS, but I doubt the result will be different.