His early appearances include episodes of The Virginian (1965) and Bob Hope Presents the Chrysler Theatre as well as the TV film The Doomsday Flight (1966) and the feature Gunfight in Abilene (1967).

Sarrazin appeared in some thrillers for Universal such as Eye of the Cat (1969) with Gayle Hunnicutt and Eleanor Parker and In Search of Gregory (1969) with Julie Christie and John Hurt.

He was originally cast to play Joe Buck in Midnight Cowboy (1969), but he was unable to gain release from a prior contract and the part went to Jon Voight.

Sarrazin starred alongside Jane Fonda, Susannah York, Gig Young, Red Buttons, Bonnie Bedelia and Bruce Dern.

Sarrazin supported James Coburn in Harry in Your Pocket (1973) and received excellent reviews for the television film Frankenstein: The True Story (1973).

He starred in The Gumball Rally (1976), then had lead roles in the Iran-shot film Caravans (1978), the Canadian mystery thriller Double Negative (1980), and the vigilante crime drama Fighting Back (1982).