The best place are the petrol stations before and after the city if you come from outside the place.
Take the bus 11 to the stade Route de Lorient. You can't miss the stop, it's in front of the stadium after 300m you will see a first traffic light it's the entrance of ring road you can start hitchhike just after, there also 3 service station before this road change into a motorway 2km further a bus stop and a lot of traffic light, the first petrol station is probably the best spot as there is traffic light before and after people are going slowly.
West towards Saint Brieuc, Morlaix, Brest
Get to the J.F. Kennedy subway station (see map). Then walk along the Boulevard d'Anjou towards the Route de Saint-Brieuc. At the roundabout, you'll find a perfect hitchhiking spot.
South towards Nantes
Take the metro towards the Henri Fréville station (see map) or bus 3 to Alma. There, walk down the Passage Henri Fréville for some meters towards a roundabout. Walk straight forward, over the motorway bridge and there you'll find a good spot to head towards Nantes. Take a closer look at the map on the right to find out where exactly.
South toward Angers
Take the metro to the last station La poterie and just walk to the roundabout, another option is to take the bus 62, 73, 75 to the town of Verne sur Seiche stop at La poste or Verne église for the 62 and walk weast to the roundabout it the entrance of a small motorway toward Angers. The bus 73 can even send you further to Corps Nuds but I've never been there, looking on googlemaps there should be at least two spot to hitchhike 2km south.
The goal is too get to the toll station just before Laval, you can easily find a car to Paris there.
Take the metro to the end station La Poterie. From here, it is about 1 km walking to the spot. Start walking on Rue de Vem to the south. To the left you will pass a huge parking place. Go past one roundabout, cross the bridge over the motorway to get to the roundabout on the other side. From this roundabout, there is an exit going on the motorway in the good direction, with a nice place for cars to stop. Use a sign with Laval written on it, if your driver don't want to pay for the toll you can ask him to drop you at the last exit before it from there you can simply walk to the toll station.
Another option is to go to Noyal sur Vilaine, there a transport company operate you can just ask truck driver at the gate or hitch on the entrance of the motorway next to it.
At the end of summer vacancy, it's also possible to find people going back toward Paris, all the tourist coming from the south of Britanny taking the N24 pass by Rennes see the West towards Vannes, Lorient, Quimper section how to get there but of course hitchhike on the other direction at the entrance of the ring road.