After I converted the files from MTS to MOV, FinalCut & QuickTime didn't recognize the files anymore.
I'm using a Mac obviously, can someone please help? Did I do something wrong or is it the software?
In most of the cases, this is a problem with the converter used to convert the MTS file. Try to adjust settings before converting. Tweak them until you find a combination to play the file in either FinalCut or Quicktime. To read more about the MOV format, use the Wikipedia's entry about Quicktime.