Strasbourg 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 a tram southwards (probably A), right to the end of the line. From there you walk west for a while, and then you can find the gas station on the side to go north.