Converting AVCHD files to mp4
Handbrake should be able to handle AVCHD files. It relies on some codec library files from VLC player, so it may help to have that installed as well. Handbrake uses ffmpeg underneath the hood.

Alternatively, AVIdemux may also be useful. It's a bit more of an editor than just an encoder, but if it can read the source files, it should be able to output the desired encoding.

Commercially, SmartConverterPro has worked okay for me.