By train
Trains leave Paris Saint-Lazare for Rouen Rive-Droite throughout the day and take about 1 hour 10 minutes to 1 hour 30 minutes. The station is about 10 minutes' walk from the cathedral and old town, or a short metro ride.
By car
The A13 motorway takes about 1.5 to 2 hours, depending on traffic leaving Paris. Use the car parks around the old town.
Making a day of it
Rouen's cathedral, the Gros-Horloge and the Place du Vieux-Marché are all within walking distance. See the Rouen map. On the way, you can stop at Giverny.