No. Nobody violates the law of conservation of energy, just like nobody expects the Spanish Inquisition. But it does seem like Christophe Hamel rises to a greater height than from where he jumped.
Julianne Dalcanton explains how the illusion is created.
One thing to bear in mind is that it is the center of mass of an object that cannot rise higher than the point from which it was dropped. In a flexible object like the human body, you can shift its center of mass by raising your arms, curling up in a ball, crouching, etc. Since observers tend to focus their attention on the head of the person they are watching, this can create gravity-defying illusions by ballet dancers and basketball players because the trajectories of their heads are flatter than one would expect for a projectile, and thus they seem to ‘float’ in the air.
Another way to rise higher than where one started from is to use one’s muscles to convert some of the body’s internal energy into overall kinetic energy, which is what we do when we jump up from a crouching position and what Hamel is doing when he sometimes pushes upwards off the side of a wall on his rebound.
One thing is clear and that is that very little energy seems to be dissipated by the trampoline itself, much less than I would have expected. Another is that Hamel’s nerve and skill are impressive.