If none of the solutions provided in the readme.txt and disabling any windows compatibility mode have worked for you (also FEAR.exe needs to be patched with large adress aware so I suggest you try to patch it yourself in case the .exe from the mod might have strangely failed to do so), the other possible solutions left for you could be to either edit the default.arch.cfg and delete "HDTextures_3.Arch00" (but you will miss some great textures from the mod) or not do any of that and play the game with texture quality set to medium (worst solution but the textures will still be better than vanilla)
For me there was one map where I had no choice but to play with texture set to medium during 2 checkpoints, so you might have to do that at some point anyway.
Panopt1c0n
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