Good free m2ts to mp4 converter?
FFmpeg should be able to do this - assuming you don't mind getting down with the command line (there may be some GUI options out there too possibly).

My Olympus E-P3 produces .MTS files - I assume they're similar (AVC/AC3 in a Blu-Ray Video wrapper).

I ran the following command:
    ffmpeg -i 00001.MTS -vcodec copy -acodec copy -f mp4 00001.mp4

That just tells FFmpeg to copy the video and audio streams but put them in a new mp4 format (the -f option).
The resultant mp4 still has the same AVC/AC3 combination but now in a MP4 wrapper.

I played both source and output in VLC and they looked the same - obviously you should satisfy yourself that quality has been maintained.
I'll wager that most GUI tools to do this task use FFmpeg under the hood.