As we know, Final Cut Pro is a non-linear and non-destructive editing software application, it can only import non-destructive video format including DV, HDV, P2 MXF (DVCProHD), XDCAM, and 2K film formats. Nevertheless, the widely used MP4 is lossy format, which is a final delivery file type and is heavily compressed. In order to successfully import MP4 to Final Cut Pro, we have to convert the lossy MP4 to non-destructive format like DV which is compatible with FCP.
just google search Step by Step Guide on How to Convert MP4 to DV so as to Import MP4 into FCP/FCE
you will find a powerful converter and a step by step guide on how to convert and import mp4 to fcp
hope it helps more or less