I agree with the comment above, 3 nights in Rouen would be a bit much for me - 2 nights is enough. The city can be comfortably visited in a day (half a day, even, if you do not visit the Musée des Beaux-Arts), and I do not find that it is a good base for sightseeing in the region because it takes a while to drive in and out of town, with some very unattractive surroundings in parts.
Actually, if you have 3 nights planned, I would rather spend them in a charming village further down the Seine, such as La Bouille, and day trip to Rouen from there + use the other day to tour the Seine valley (there are several amazing abbeys) and/or visit Le Bec-Hellouin, a well-preserved village.
By all means take the train from Paris to Rouen and rent the car there, it will be safer, and there is no need to pre-book the train from Paris to Rouen: there are 1-2 trains per hour, seating is unassigned, and same-day prices are relatively low. The only problem is if you arrive on a Sunday (no car rental offices in Rouen are open that day), in which case you might as well stay in Rouen and rent a car as you leave town.