Fischer was a successful restaurant owner based in Zürich. Around him he assembled Écurie Espadon — the word meaning "swordfish" in French — as the entry name for a small group of Swiss amateur privateer racers. The team began with French machinery, predominantly Gordinis, which lent it the French "Écurie" prefix. As equipment shifted toward Italian cars, principally Ferraris, the name evolved to Scuderia Espadon, reflecting the Italian equivalent. Team members drawn from Swiss business life included Rudolf Schoeller; Peter Hirt, a wealthy businessman from Küssnacht involved in precision tool manufacturing; Peter Staechelin from Basel; Max de Terra; and Paul Glauser. Fischer was himself the team's fastest driver.
Fischer was racing by at least 1946–1948, when he began with Simca-Gordini machinery. By 1949 he raced a HWM in the Prix de Berne, finishing sixth and sharing a drive with Stirling Moss. He entered various non-championship events on borrowed and hired Gordinis before ordering his own Ferrari 212 — a specially-built customer car powered by a V12 2540cc engine — for a full programme in 1951. That season he accumulated a series of strong non-championship results: third at Syracuse and San Remo, second at Bordeaux, and fourth at Zandvoort. In the World Championship itself he finished eleventh at the 1951 Swiss Grand Prix and sixth at the German Grand Prix at the Nürburgring, starting from eighth on the grid. He also won three Formula Two events: at AVUS, Aix-les-Bains, and Angoulême.
For 1952, Ferrari provided Fischer with a customer version of the Ferrari 500 F2 — the same model the factory team was using to dominate the championship, which that year ran to Formula Two regulations. The car was numbered 184F2. The season proved Fischer's finest.
At the 1952 Swiss Grand Prix at Bremgarten, Fischer finished second, behind the works Ferrari of Piero Taruffi. The following month he took third place at the German Grand Prix at the Nürburgring — a circuit demanding sustained precision over its numerous corners and undulations, and one where driver skill tended to differentiate results over the course of a long race. He accumulated ten championship points to finish fourth in the World Drivers' Championship, equalled that year among private entrants only by the emerging Mike Hawthorn.
Fischer also won two significant non-championship events in 1952: the Eifelrennen at the Nürburgring and the AVUS race in Berlin. At Rouen-les-Essarts he suffered engine failure in the Ferrari 500 and was forced to share the older 212 with Peter Hirt, finishing eleventh. His World Championship campaign ended with a retirement at the 1952 Italian Grand Prix at Monza.
At the close of the 1952 season, Fischer abruptly retired from international racing at the height of his form. The evidence for the quality of his driving came afterwards: the Ferrari 184F2, subsequently entered by Écurie Espadon for Peter Hirt in 1953, produced no notable results, strongly suggesting that Fischer's 1952 results were the product of his own ability rather than the car's. He participated occasionally in Swiss hillclimbs in later years. He died on 30 December 1976 in Lucerne, aged 64.
Fischer is remembered as an exceptionally capable gentleman racer who, competing without the resources of a works team, brought a privately entered programme to the verge of championship contention in one of the most competitive periods of early Grand Prix racing.