I struggled for about 8 hours today trying get FCPX to read my MPEG-2 video files from the old camcorder (copied over onto the Macbook running El Capitan). Trying every solution that I could find including those from 2012 which are still present on the Apple Forums, downloading more than one dicey, third party software that doesn't work, chasing fantasies about "easy to use" or "free" converters available on the internet. I also bought one from the App Store on Apple, which was advertised as a "quick and easy" solution to this problem. Nada - nothing. I pretty much gave up and thought the kids birthday parties from years ago will just have to be stored in my own biological memory. I was even willing to buy another camera and play the movie on a TV and re-record it onto another camera with a movie type that FCPX would support.
But, I ended up doing two things. First, I used Quicktime version 10.4 to open the old MPEG-2 movie, then used QT's Export function to convert the movie to a .MOV file, which FCPX could understand. It worked. This was satisfying to finally find such a solution after so many hours of research, false leads, cost, and substandard, buggy software trials.
The icing on the cake, though, was when I read your post, Jowie, about changing the file extension.
IT WORKED PERFECTLY!! I first copied the movie to the desktop so that if anything didn't work, I still had the old .MPG still there. I changed the extension but it didn't work right away. I used the "Get Info" function to make sure the file name "really" was changed to .MOD, because the way my operating system shows files, when I changed the file extension, the end result was that it was really only adding .mod to the middle of the file name and keeping ".mpg" hidden.
Another little spike of worry was when the preview thumbnail in Finder changed to an .exec -style thumbnail picture. However, FCPX knew just what to do with it. I now have all the old home movies ready for processing. I feel like I've defeated Goliath with Jowie's simple fix.
Thank you Jowie for posting your solution here on the forums - now all the world who has old MPEG-2 videos (probably people close to 50 years of age like me) can benefit from your simple gift. Kudos to you and of course Apple for maintaining this forum.
ADK-Mark