Lodging in Rouen

Some confusion in your question. Avignon has two train stations, one just outside the city walls for regional trains and one on the fringe for TGVs. I assume the latter is where you arrive from Rouen but I can't guess where you will depart the next day. The TGV has car rental offices, plus a shuttle bus for the short ride into the city, arriving near the old station. If you are spending your day in Avignon, which is both easy and worthwhile on foot, you certainly do not want a car as parking is very difficult unless you are outside the walls. Anyhow you can walk easily enough in the morning to the central train station or take a cab, while a taxi to the TGV station rather than the shuttle is also possible.
The helpful tourism office website is http://www.avignon-tourisme.com/home-1-2.html

I think Jim is looking for a hotel near the train station in Rouen. I can't help, but maybe someone else can.

Adam is correct. I am trying to locate a place to stay close to the Rouen train station since we have an 8:45 AM train. It is the only direct train to Avignon from Rouen and we don't want to miss it. We also get into the Avignon TGV station about 2PM on a Friday and don't have to be at our B&B in St. Remy until 4PM the next day. Since we don't pick up the car at the TGV until Saturday afternoon I thought we might take advantage of that time to explore the city with public transportation instead of trying to drive back there in the middle of our Provence stay. We have tried to stay near train stations in the past and had a mix of good and not so good. Any help will be appreciated.

Can't help with the hotel since we only visited Rouen as a day trip. However, I would suggest not going there until about mid-afternoon. Linger longer in your previous location because Rouen only needs 2-3 hours to see its major attractions. Walk down the historic street past the cathedral to the plague site if that interests you. Stop and admire the cathedral which Monet painted repeatedly. Head the other direction on the street and see the overly commercialized area where poor Joan died after the rotten king refused to pay her ransom. Have dinner near the cathedral....that's about all we found of interest in Rouen which is a large city....Honfleur, Bayeux, St. Malo, Jumiergees Monastery(sorry, not spelled correctly), Les Andeleys are far more deserving of the earlier part of your day.

I have only once been to Rouen and we stayed at the Hotel de la Cathedrale, across the way from the Cathedral itself. I know we walked from the train to the hotel but it was a rather long walk, as I remember, but couldn't you take a taxi in the morning to the station ? The hotel was very pretty and comfortable, by the way.

I completely agree with Cynthia's comments. The cathedral and plague site and old section are worth a short visit but Rouen is not charming-the modern church is boring. The creperie (in the old town)that was in RS guidebook was very good.