You don't just drag and drop it. That camera shoots XDCAM, so you either use the XDCAM TRANSFER UTILITY...separate software...to convert that to Quicktime that FCP can work with. Or you use the XDCAM Log and Transfer plugin and use Log and Transfer in FCP to bring in the footage.
You can't import those MP4s to FC. You can't even open them with QT Player.
You need to install the SONY Transfer software and use the Import XDCAM option that you will get in FC.
You need to have the full file/folder structure from the camera.