Thanks for all your help ! I don't think that I'll have the time to change the pair any soon, but I'll let you know how it went and if the BSOD stopped.
Well, I bought the new pair a few months ago, and the BSOD started not so long after (I never had any BSOD before) so I'm pretty sure that it is coming from these 2 sticks, so I'm just going to buy a new pair.
Well I didn't have any BSOD since the chkdsk but it happens randomly, so sometimes I don't have any BSOD for 2 or 3 days, then it happens again. So I'm still going to run the memtest just in case it comes from the memory.
I'm not at my home at the moment and I don't really know how to explain my problem, so I'll take a picture of it to make it more clear once I come back.
I've installed Memtest on a USB drive and went in the BIOS to use the boot override so that it boots the USB drive instead of the OS drive, but the OS is still the one that is booted first. Do you know why ?
Well, it said that Windows made some corrections on the files, and that no other actions were required. So I guess that the files are repaired now. I am going to run the Memtest now.