h264 is the encoding used in MPEG-4. Seeing that I knew that I should be able to just re-encapsulate it in an mp4 file.

The ffmpeg command I used should have simply copied that stream into the output, without recoding - and I think it did. But comparing the video steams in the input and output, there appear to be differences. How can 29.97 fps (frames per second) become have become 59.94 fps? Or is that an error in the reporting - there are a lot of '59.94' values in there?

And I just noticed that the audio has been recoded - from 'Audio: ac3' (which is Dolby) to 'Audio: aac'. If I add -c:v copy I can avoid that and the process becomes instantaneous.