Saumur has a train station on the north bank of the Loire, a short walk across the bridge from the old town. Regular TER services connect it to Tours (about 30 minutes) and Angers (about 20 minutes), both of which have TGV connections to Paris. From Paris Montparnasse you can reach Angers in under 90 minutes and change there for Saumur.
By car, Saumur sits just off the A85 motorway and is about three hours from Paris.