So I've been measuring at some points on the circuit and it seems that the H-bridge is eventually broken :~
I've joined once again some photos of my measurements with the multimeter to be clearer but, as I understand the situation:
- 5v power flows through pin 9 of the Arduino, which is suppposed to power pin 1 of the H bridge
- 5v power flows through the wire between Arduino's pin 9 and H-bridge's pin 1
- but in the meantime almost no power is measured through pin 1 of the H-bridge.
I haven't enough experience in H-bridges to be sure (it's the first time I use one !), but I think it means it's broken (why would it measure near to zero then ?). 
I should receive a new h-bridge on Monday, so we'll can figure out if the problem really comes from it (although if it doesn't solve the problem, I'll really be at a loss 
)
