I just fixed the problem, it's indeed a BattleEye bug ! It seems they have a problem with the Windows Driver Verifier and for some reason it was enabled on my system.

Yup, it seems to be coming from "arma3battleye.exe" when I launched that, my PC bluescreened after a few seconds. So it seems to be a problem from BattleEye ? Starting the BattleEye service (BEService) in the task manager manually doesn't crash my PC though.

Just tried that. Closed Steam, restarted it with right click -> start as admin, then launched Arma 3 from the launcher, it blue screened again.