The proper way to mount non-AI lenses on the FE is to first raise the little coupling lever on the lens mount (located at about the 2:00 position). Press the button beside it and lift it out of the way, then mount the lens. Metering would then be done by stopping the lens down to take your reading. If you don't raise that lever the FE won't meter correctly with non-AI lenses unless you stop the lens down (except when you happen to be shooting wide open).
Originally Posted by ColdEye
The same is true for the FM but not for the FE2 and FM2 which don't have that little lever on their lens mounts. They were intended to be used with AI lenses only.
The Nikkormat EL/ELW models do provide AE or normal metered-manual without any stopping down required with non-AI lenses or any Nikon mount lens having the meter coupling prong.