What is the best free program to use to reduce the resolution of DivX video files ?

I have a lot of MP4 files that I'd like to watch on my large TV using my DVD-player. The DVD-player has a USB-in port and plays AVI files no worries, but the only other video format it can play is DivX. So I successfully converted the MP4 files to DivX, but the DVD-player still cannot play them, apparently because the resolution of them is too high.
So I need a good free program that either:
Converts a high definition MP4 file to a low-definition DivX file,
OR
Converts a high-definition DivX file to low-definition DivX file.
Any advice would be much appreciated.