1963 and 1965 were probably Simpson's best years for Classic races. He was riding for the Peugeot BP team in 1963, when he won the gruelling motor-paced event Bordeaux-Paris, was second in Paris-Brussels and Paris-Tours, third in the Ronde van Vlaanderen, 8th in Paris-Roubaix, and 10th in both La Flèche Wallonne and Giro di Lombardia.