Hmm, ok, thank you for your feedback, in order to be sure I'm going to restart from scratch and I'll see...
What's weird is that the backups I'm trying to restore have been made right after the template installation so I can be sure the website was still fresh and ok at this time, and I have already restored the very same ones in the past without any issue ; hence my doubts.
Anyway, thank you very much for your answers and have a great day !