It seems that there is no correct video codec on the computer for FCP to afford the video. Have a try to encode MOV to Apple ProRes via a third party program, like HandBrake and Brorsoft Video Converter for Mac.
According to Apple support website, Final Cut Pro does support importing and editing QuickTime movie files. However, .mov is just a wrapper. The bigger and better question is what’s inside the wrapper (commonly called a codec). So you can have a .mov file that uses different codecs. It could be DV, HDV, XDCAM, DNxHD, ProRes, DVCPRO, etc. Each of those are different codecs that a .mov can contain. some MOV files from Canon/Nikon can’t be ingested by Final Cut Pro correctly, due to its heavily compressed H.264 codec. To import MOV into FCP X smoothly, you need to transcode MOV to ProRes for FCP with Brorsoft Video Converter for Mac- one of the best MOV Decoder/Encoder.