Chrétien was educated at the École communale in Ploujean, the Collège Saint-Charles in Saint-Brieuc, and the Lycée de Morlaix.

He entered the École de l'Air (the French Air Force Academy) at Salon-de-Provence and graduated in 1961, receiving a master's degree in aeronautical engineering.

In 1977–1978, he was appointed deputy commander of the South Air Defence Division in Aix-en-Provence, and he served in this position until his selection as a cosmonaut in June 1980.

Soyuz T-6 was launched on 24 June 1982, and Chrétien, Vladimir Dzhanibekov and Aleksandr Ivanchenkov linked up with Salyut 7 and joined the crew of Anatoli Berezovoy and Valentin Lebedev already on board.

Together with Alexander Alexandrovich Volkov and Sergei Krikalev, he linked up with Mir and joined the crew of Vladimir Titov, Musa Manarov and Valeriy Polyakov already on board.

They spent 22 days carrying out a program of joint Soviet-French experiments, including a 5-hour and 57-minute EVA by Volkov and Chrétien during which the two men installed the French ERA experimental deployable structure and a panel of material samples.

He served on the crew of STS-86 Atlantis (25 September to 6 October 1997) the seventh mission to rendezvous and dock with the Russian Space Station Mir.

In September 2000, while visiting a Home Depot store in Webster, Texas, he was hit by a 31 kg (68 lb) drill press that fell from a shelf more than 3 m (9.8 ft) above him.

The injuries to his neck, head, and shoulders were severe enough that a NASA flight surgeon determined that Chrétien could no longer fly.