Hey Benoît!
Let me add some suggestions that might enhance the tune.
1. The piano accompaniment could stay as simple as it is, but I would advice playing around with note velocities. Currently all notes are of the same velocity which makes it sound very mechanistic. Instead, one can put emphasis on a dominant note and make the rest quieter, or make velocities change - become quieter or slower. This is especially important when your piano sounds on its own, in the beginning.
2. Compositionally I would not have the piano in the beginning. It is just way too simple for that. The piece is rather slow and I felt that such a slow start might put listeners off. I would also rethink the development of the tune. It sounds like a soundtrack piece, and there is some interesting development in the middle, but this kind of tune could benefit from much more variety, both melodic and compositional. Change of tone, pace could be extremely beneficial here.