It looks like I didn't search properly, I apologize for that.
I've just tried lowering my windows audio bitrate to 16 bit and 44100Hz, and now it's playable again. However, I still lose around 10 FPS while shooting, depending on the game mode.
Thanks for answering so quickly.

Yes, I forgot to mention that on the additional information. I've also tried loading ARMA 3 without any mods enabled, no success. Still have the same problem.
It's really annoying, some missions/mods are barely playable because of this issue.

If you have Ares module, you are able to do that.