Strassbourg is one of the bigger cities of France. It is the siege of the European Parliament, and pretty bourgeois.
In theory it seems doable to hitchhike directly from the centre, as there is the entrance to several highways. However, the people of the city are not very hitchhike-friendly, so it is better to directly go to a gas station on the highway.
For going north
Go south, taking tram A (I forgot, please confirm someone), right to the end of the line. From there you walk west for a while, and then you can find the gasstation on the side to go north. (I'll upload some pics :)