You are seeing 0v across VCC and GND when you have it hooked up? Or you are seeing 0v on the blue screw terminals on the far side?
I assume your 3v is fine and the problem is triggering the GPIO. For that you need to put your meter between GND and pin 24, then turn pin 24 high and low:
gpio mode 24 out
gpio write 24 high
# ensure meter shows 3v here
gpio write 24 low
# ensure meter shows 0v here
Make sure that works before looking at the blue screw terminals. In fact, you don't even need the relay to ensure this.
These are assuming you are using physical pin 24; if you are using BCM pin 24, do this:
gpio -g mode 24 out
gpio -g write 24 high
# ensure meter shows 3v here
gpio -g write 24 low
# ensure meter shows 0v here
If this doesn't work, you'll need to describe/illustrate it better or hope that a french speaker can help you in your native language.