No power after changing an outlet
After long hours of testing, it happened that the lunatics that made my installation actually switched the live wire and the pilot wire on the main panel's differential.
This is very misleading and seems utterly dangerous as this wire is shared among several outlets. Therefore, despite turning the power off on another outlet, my pilot wire was powered on and could have shocked me!
Healthy fear and respect indeed. Respect for the power of electricity, and fear for the incompetence of others.