Streiff was a late starter in motorsport. In 1977, at the age of 22, he won the Volant Motul competition at the Nogaro racing school. He began racing in Formula Renault in 1978, winning his first race at the French Grand Prix meeting at Paul Ricard. After finishing fifth in the series he moved to European Formula Three in a privately entered Martini-Renault. Switching to a Toyota engine made him more competitive and in 1980 he beat the Martini factory team at Zolder. In 1981, driving a Martini-Alfa Romeo for the Ecurie Motul Nogaro team, he won the French Formula Three Championship. That same year he finished fourth in the European Formula Three Championship, taking second places at Zolder and Imola.
He graduated to Formula Two in 1982 with Henri Julien's AGS team. In his first season with a new teammate, Pascal Fabre, the pair scored a podium in the Gran Premio di Roma at Vallelunga, finishing second and third behind Corrado Fabi's March. Streiff ended the year sixth in the championship. In 1983 he finished fourth overall, his best result a second place at Pergusa. In 1984 the team secured backing from Gitanes, Blanchet Locatop, and Elf, and Streiff won the final round of the European Formula Two season outright at Brands Hatch — his maiden single-seater victory.
Alongside his single-seater work, Streiff made four starts at the 24 Hours of Le Mans. In 1981, driving a Rondeau M379C-Ford Cosworth for Jean Rondeau alongside Jean-Louis Schlesser and Jacky Haran, he finished second overall, first in the GTP class, behind the winning Porsche of Derek Bell and Jacky Ickx. In 1984 he returned to the podium, finishing third overall in a Skoal Bandit Fitzpatrick Racing Porsche 956 shared with David Hobbs and Sarel van der Merwe.
His Formula Two win at Brands Hatch in 1984 earned him his Formula One debut: Renault entered him in a third RE50 for the Portuguese Grand Prix at Estoril on 21 October 1984, where he qualified 13th before retiring with transmission problems on lap 23.
In 1985 he drove for AGS in the newly introduced International Formula 3000 series, finishing eighth. Partway through the season, Ligier signed him to replace Andrea de Cesaris for the final rounds at Monza, Spa, Brands Hatch, and Adelaide. At Adelaide, in the season finale, Streiff finished third — the best result of his Formula One career. During the final laps he had attempted to pass team-mate Jacques Laffite for second place; the two Ligiers made contact, and the front wheel axle of his Ligier JS25-Renault was severely damaged. With Ivan Capelli a lap down in fourth, Streiff managed to hold on, the wheel bouncing across the final lap while remaining attached. Team owner Guy Ligier, unimpressed, did not offer him a drive for 1986. He had already made a one-off appearance for Tyrrell at the 1985 South African Grand Prix.
He signed for Tyrrell for 1986 alongside Martin Brundle, taking seventh in the opening race in Brazil and scoring points finishes including sixth in Britain and fifth in Australia. He remained at Tyrrell for 1987 alongside Jonathan Palmer, taking sixth in France and fourth in Germany. In 1988 he returned to AGS, which had moved up to Formula One. The underfunded AGS JH23-Ford Cosworth produced no points that year, his best result an eighth place at Suzuka. After Suzuka he was invited to share a factory Sauber-Mercedes C9 with Mauro Baldi in the 1000 Km of Fuji, but the car retired with brake failure.
For 1989, AGS planned a full season with Streiff and Gabriele Tarquini. Testing began at Jacarepaguá in Rio de Janeiro. On 15 March 1989, three days before the opening round of the season, Streiff crashed heavily at the fast right-hand kink before the hairpin onto the back straight. The roll-bar of the AGS broke on impact; the car rolled multiple times, losing its engine, gearbox, and all four wheels, and ended up over the guardrail. The marshals who reached him first righted the car, pulling his helmet off in the process. He was then laid on the grass before an ambulance arrived, and the subsequent road to the hospital was prolonged when the helicopter pilot, unfamiliar with Rio, landed first on Copacabana beach before locating the correct hospital. The delay and the handling of him at the scene were later identified as having worsened the spinal damage. He sustained a broken shoulder and two fractured vertebrae in his neck and was left paralysed and quadriplegic.
His recovery extended over two full years. During this period all the Formula One drivers at Suzuka donated money toward his medical bills. Nicolas Sarkozy, then mayor of Neuilly-sur-Seine, organised a police escort for the ambulance taking him to the specialist care unit in France. He only returned home, in an adapted dwelling, in 1992.
Streiff organised the Masters Karting Paris-Bercy indoor karting competition from 1993 to 2001. The inaugural 1993 event included Alain Prost and Ayrton Senna racing against each other — the last occasion the two did so. He later opened Streiff Kart, a karting centre north of Paris, and ran a business converting vehicles for disabled users. In early 1994 he and Hugues de Chaunac made a bid to purchase the Ligier team, supported by Williams, but the bid was rejected.
He dedicated his later years to raising awareness of disability issues and road safety. In memory of his accident, a street in Wingfield, South Australia, was named after him. Belgian blind speed record holder Luc Costermans dedicated his 2008 world blind road speed record to Streiff.
Philippe Streiff died on 23 December 2022 in Puteaux, Hauts-de-Seine, aged 67. He was survived by his wife Renée, their sons Romain and Thibaut, his mother Michèle, and his brother Pierre.