Strasbourg is one of the bigger cities of France. It is the site 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 northEdit
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 gasstation on the side to go north.
For going east (Germany A5)Edit
You can take the regional train going to Kehl which is already in Germany (around 6 minutes for 2-3 euros). In Kehl you've got a big road going directly to the motorway A5 - and everyone who's coming from France is using this road. You also find a gas station!