Something is not right here. The ground does NOT pass THROUGH the GFCI and hence it cannot have 120V from the GFCI or elsewhere unless it's open or a ground could be connected to 120V somewhere but a properly wired GFCI does NOT pass the ground through and a correctly wired ground coming into a GFCI will be "earth ground" and not be at 120V.
A GFCI does have a ground connection for the ground lug and modern GFCI's can also detect a neutral to ground fault. A GFCI does pass through the hot and neutral and in fact detects a current difference between these two wires. Perhaps there is a wiring problem upstream or the wiring colors are misleading vs actual connections or ???
