It actually depends on the game though. The more the player can see, the more the computer has to do to render in those objects, therefore FPS will be lowered/impacted, if FOV is higher.
This is simply because the game will now have to render more of the world in front of you, it has to render more elements, Textures, Assets, etc.. This can be quickly measured and confirmed by looking at the increased load on your CPU/GPU while maxing your FOV.
FOV increase will actually stress the CPU culling and GPU vertex processing which typically are 5-15% of a normal frame. In culling, the CPU decides what needs to be sent to the GPU, so some games might be bound by drawcalls, so this is where FOV hurts FPS.