Ballisat was born in Sutton, Surrey, on 20 May 1928. He married Betty Webley in 1960. His competitive motorsport career developed in the late 1950s through a combination of circuit racing and rallying, representing the Standard Motor Company through its Triumph brand before moving to the Rootes Group and the Sunbeam marque.
Ballisat was most consistently active in international rallying between 1958 and 1962. In 1958, co-driven by Alain Bertaut in a Triumph TR3, he finished fourth overall in the Coupe des Alpes, and also contested the Deutschland Rallye with Peter Roberts, finishing tenth. In 1959 he achieved his best rally result when he and co-driver E. Marvin took a Triumph TR3A to second overall in the International Tulpenrallye. He also started the Monte Carlo Rally, the Liege-Rome-Liege — where he finished eighth — and the Tour de France Automobile that year.
His rally activities continued into the early 1960s under Rootes Group colours. Driving Sunbeam machinery, he finished sixth in the 1961 Acropolis Rally alongside Peter Jopp, and seventh in the 1961 Coupe des Alpes with Tiny Lewis. He entered the 1962 Tour de France Automobile again with Lewis.
Ballisat also raced single-seater cars in non-championship Formula One events during this era. Driving a Cooper T43, he appeared at the Grand Prix de Caen in 1958. In 1960 he finished seventh in the Lombank Trophy and sixth in the Crystal Palace Trophy in the same car, and also contested the Lavant Cup and the Norfolk Trophy. None of these results counted towards the Formula One World Championship.
Ballisat competed at the 24 Hours of Le Mans on four occasions across a five-year span.
His best result came in 1961 when he and co-driver Bolton finished ninth overall in a Triumph TRS entered by the Standard Motor Company factory team. In 1960 he and Becquart started in a Triumph TRS for the same team, but the car was not classified at the finish. In 1962 he was entered by the Rootes Group to drive a Sunbeam Alpine with Tiny Lewis, but the car did not start. His 1963 Le Mans entry — again a Sunbeam Alpine — retired during the race. In 1964 he drove a Sunbeam Tiger for the Rootes Group with Henri Dubois but retired again.
Beyond Le Mans, Ballisat and Les Leston finished 34th at the 1961 1000 Kilometres of Nürburgring in a Lotus Elite, and he took 11th place in the 1962 Tourist Trophy at Goodwood driving a TVR Grantura.
After retiring from competition, Ballisat worked in the oil industry for a number of years, maintaining involvement in Shell's racing-related activities. He died in Bridgwater, Somerset, on 25 May 1996, aged 68, following a period of illness.