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To get on the A7, you have two possibilities : Valence Nord (North) or Valence Sud (South). I much prefer the on-ramp at Valence Nord, because there's more space for cars to stop. I never waited more than 30 minutes at this spot. I use it to either go North or South, but most cars are going North. I have to sometimes decline a few cars going North if I want to go South, but I always end up finding a car rather quickly. Going South : The first service area is soon after Valence South, so if a car is going past Valence accept the ride, and get dropped at this service area to search for another car. Going North : Most cars are going to Lyon, and if you don't you'll have to get down at the toll near Vienne (there's a parking area with a few cars) or before in a bigger gas station.
South towards Marseille, Montpellier, Barcelona
It is actually very easy to get to the first service area south of Valence, in Aire de Portes-lès-Valence, by taking the city bus. As of November 2019 the fare is 1.4 euros and the bus route is number 10. It runs every 20-30 minutes, passing right in front of the Valence Ville station in the centre. Full details can be found here.
You take it to the very end, getting off at the stop d'Orves (the bus does a little loop and passes the same spot as the second to last stop out of Valence and first on the way back in, as the map in the above link demonstrates). From there you walk west on Rue Estienne d'Orves to Route Nationale 7, cross the A7, and then turn left down the road that you see immediately after crossing (there will be a little shortcut trail at the bend there). Continue down this road and you get to the gate for the service area. Though the gate looks imposing upon approach, when Movethathoof passed through in November 2019 he found the gate without a lock; there was a place for where it may have once been, but it now just pushes open.
From this station there is lots of traffic to Marseille, but much less toward Montpellier and Barcelona. Movethathoof was quickly offered many rides to Marseille on his way to Montpellier, and decided to take one to get to the final service area before the road splits. This service area, Aire de Mornas Village, is around 80 kilometers further down the road, just before Orange. It is much bigger, with more traffic (including a much larger area for trucks), and though he was again offered many rides to Marseille first, he did get a ride quite quickly to Nimes. The roundabout before entering the highway doesn't leave a lot of space for people to stop, but that didn't stop many people from stopping to offer a ride.
Note: Neither of the above mentioned service areas have easily accessible recyclable containers; if you'll need cardboard for a sign you might be better served finding it before heading there.
There's a massive roundabout near the shopping area "Les Couleures". There's a bus stop not far from there. You can stand at the entrance of the national road N532 towards Grenoble. It becomes a highway after 30-40 kilometers, but there are a few service areas in between. There's enough space for cars to stop.
Accommodation and Sleep
You can probably get away with camping for a night near the Rhone river.