Nantes is a city in western France of roughly 600,000 inhabitants.
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North towards Rennes
Take the tramway number 2 and get off at "Le Cardo". 20 meters behind you you will see the road going to Rennes. This is a very famous spot which works very well. Cars have place to stop and as there is a roundabout they are not going fast yet.
North West towards Saint-Nazaire, Vannes, Brest
There is a nice spot at the commercial center Atlantis. You can reach it with the tramway number 1, get off at the terminus "François Mitterand". Once there, you follow the railways until the next cross-way (20m), there turn right. On the third roundabout is the sublet to the N444. The walk might take you 5 to 10 minutes.
South West towards Noirmoutier, Pornic, Saint-Brevin
Take the Tramway line 3 to Neustrie (the terminus), walk slightly back the way you came and take the road to the left, Rue de la Baronnaise continue past the first roundabout and down Rue de la Pierre. After about 10-15minutes you will arrive on Route de Pornic at a large roundabout which slows traffic, place yourself there or alternatively at the gas station a little further along, the round about seems to work best.
Take the BusWay (line 4 of tram network) to Bourdonnières, cross the carpark and wait at the small roundabout, on Boulevard de Vendee. The first petrol station leaves you on the A83, the motorway towards Niort. There's also the peage [toll booth] about 5-10km down the road - from there you can find long distances rides with a sign for Bordeaux.
Another easy way is to take the BusWay, line 4, and stop at Clos Thoreau bus stop. In front of this busstop, on the Boulevard Emile Gabory, you hitchhike with a sign for Niort or Bordeaux, near the walking path, and just before the supermarket parking entrance, so that the cardrivers can stop. See on map : 
Option 1 Close to city center, if you are lucky
Take the tramway number 1 and get off at Bd De Doulon. Go down the street to the roundabout at the junction with the Boulevard De Sarrebruck. There you can start hitchhike, you can be seen and cars have space to stop.
Option 2 On the tramway line : Leclerc gas station
Take the tramway number 1 and get off at Haluchere. Cross the tramway rails: the road ahead is Route De Paris, the old road to Paris. If you don't go further then Angers, you can try on this road: continue north-east and you will find cars at the Leclerc petrol station (see below).
Option 3 Safest option : at the junction light
For more distant destinations, it is better to take the highway at the junction 4 km further on Route de Paris. Once you are at the junction, stand at the red light in the middle of the road, in the lane which turns left towards Paris. The cars turning here go all on the highway. You can walk along the lane with your sign when cars are waiting.
To get there, from Haluchere:
A) walk Route de Paris about hour
B) take bus 77 to Cifam, then 5 minutes walk on the Route De Paris to the traffic lights (bus runs only on working days)
C) take bus 85 to Parc (every day, 2/hour) , then 5 minutes walk Rue Des Carrières till it goes along the Route de Paris, cross the bushes to join it, take on left and walk till the traffic lights.