Hi. The JVC format always was problematic. FFmpeg based encoder and converter are usually compatible with it. Try this one:
THe VLC video player should also be able to play them:
Note that the .moi is just an associated file and the real video file should be a .MOD or .TOD
Yes those are free (i always advise opensource software to anything else). They are for PC that said.
iSkysoft have a video converter called "video converter" for Mac and is also available for windows. They mention MOD and TOD have compatible files so it should work. The conversion is usually not very long as those format are really mpeg2 files.