I downloaded Handbrake as you supposedly can covert video files to .MOV with it. However after importing MP4 and MTS files I do not have that option in the output settings or the toggle presets to do so. Am i missing something here?
Then HandBrake is not the option, as it does not provide the correct editing codec for FCE, called Apple Intermediate Codec (AIC).
For that you need MPEG Streamclip.
Or you could try Log & Transfer if you still have the camera and the SD cards.