Your Coppermine gallery might need a plugin or extension to handle .mp4 files properly. Coppermine is great for images but sometimes needs a little extra for video playback. Check the Coppermine plugins repository for a video player plugin that supports .mp4 files. I had the same problem a while ago; the only way to solve it was by using a video editing platform.
Well, after long searches, I came across this free movie maker called Movavi, and it's very nice; you should check it out. I figured out what and how to do everything in less than half an hour.