Thanks again for all your suggestions. I think you made a point with the relays, there is no little "tick" sound anymore when I turn the lights on... And it would make sens why the blue light doesn't work on the dashboard anymore I guess?
I don't have a multimeter unfortunately, and I couldn't figure out where the relays were, and since I wouldn't know what to do even if I could find it...
By switch you mean the stick we turn to put the lights on? It seems to work since the parking lights and the back lights also work (both parking and "road" lights)
I will bring the car to the garage tomorrow, I have to do some road at night on Tuesday. I thought it would have been an easy thing to fix with your knowledge, but it stops where mine ends, so almost at the beginning...
I will come back anyway to tell what the garage said, if it can help somebody else... Thanks a lot guys.