Hi,
I recently ran into problems with .mts files. I had no idea where they came from, what camera, etc. It was only a folder with a bunch of .mts files. (It was not in its original folder either as it records from camera)
I downloaded the plugins that I could find for FCP and tried Log & Transfer but no luck.
I tried MPEG Streamclip, Compressor and a few other programs to transcode to Prores but no program recognized the files.
Luckily I have Premiere Pro CS6 (Believe CS5 and up will work) and it recognizes almost any file format so I imported into PP and then exported as a ProRes file. That file was hen imported into FCP.
There could be better ways but I had no time and was the easiest, quickest option for me.
Good luck