I tried with another video and now it works. It is also an .mp4, but it is a light movie (only 5 MB), while the other one is 580 MB! So the problem must be the weight file.

The video will stream (on www.neu.globalboys.ch/index.php/globalcup) on Chrome and IE.

It is not an issue of the extension or of how you encoded your video. Firefox does not support mp4 videos.

It will start supporting them from the next version.
caniuse.com/#search=mp4