Frank was born in Glendale, California to musician Jack Marshall. He entered the film world when his parents invited him to a birthday party for the daughter of directing legend John Ford in 1966. There, he met Peter Bogdanovich and soon agreed to work on his first film, Targets (1968), later followed by collaborating on The Last Picture Show (1971) and many other films.

Continuing to branch out into the industry, he served as line producer on Martin Scorsese's The Last Waltz (1978) and associate producer on Walter Hill's crime thriller, The Driver (1978). Marshall first worked as executive producer on Hill's cult classic The Warriors (1979). While producing the iconic Raiders of the Lost Ark (1981), he met Steven Spielberg and their future wife Kathleen Kennedy, and Frank himself was hired to join the Amblin Productions company in 1980.

He continued producing memorable films with Spielberg including Poltergeist (1982) and Twilight Zone: The Movie (1983) (while Kennedy separately produced E.T. the Extra-Terrestrial (1982)). He worked as executive producer on Indiana Jones and the Temple of Doom (1984), Gremlins (1984), The Goonies (1985) and the Back to the Future (1985) trilogy.

He married Kathleen Kennedy in 1987, and after producing numerous films, he made his feature directing debut with Arachnophobia (1990). Reacting to the success of his directorial debut, he left Amblin in 1991. In 1992, The Kennedy/Marshall Company was formed, and the next year they released its first film Alive (1993), directed by Marshall. Both Kennedy and Marshall signed deals with Paramount in 1992, at the same time the company was formed. His productivity has only increased since then, as he took over primary duties of the production company since Kennedy was named president of Lucasfilm in 2012.