French was born and raised in Holyhead, Anglesey, Wales, and educated at the independent St Dunstan's Abbey (now Plymouth College) boarding school on Craigie Drive in Plymouth, Devon. Her father, Denys, was a member of the Royal Air Force being stationed at RAF Valley. The RAF partly funded her private education but she did not enjoy her schooldays. She later won a debating scholarship that brought her to study at the Spence School in New York. There she met an Irish sailor called David White and was briefly engaged to him.

French's confidence and self-belief stems from her father who told her how beautiful she was each day. She stated "He taught me to value myself. He told me that I was beautiful and the most precious thing in his life." He had a history of severe depression and attempted suicides but managed to conceal his illness from French and her brother. He committed suicide in 1977 when French was nineteen and he was forty-five, having left the RAF.

French has had an extensive career on television, debuting on Channel 4's The Comic Strip Presents series in an episode called "Five Go Mad in Dorset" in 1982. Each episode presented a self-contained story distinct from other episodes, and showcased Comic Strip performers Peter Richardson, Rik Mayall, and Robbie Coltrane and Adrian Edmondson, in addition to French and Saunders.

She acted in twenty-seven of the thirty-seven episodes, and wrote two of them. One week featured a parody of spaghetti westerns, and another, a black and white film about a hopelessly goofy boy. Some of French's first exposure to a wider audience occurred when comedy producer Martin Lewis recorded a Comic Strip record album in Spring 1981, which featured skits by French & Saunders.

French has co-written and starred in her own successful comedy series French & Saunders with Jennifer Saunders, which debuted in 1987 and still airs sporadically to this day. On their show, the duo have spoofed many celebrities such as Madonna, Cher and Catherine Zeta-Jones and they have also parodied films in the series such as The Lord of the Rings, Star Wars and Harry Potter and the Chamber of Secrets. After twenty years of them being on television together, their last sketch series, A Bucket o' French & Saunders, began airing on September 8, 2007.

French and Saunders have also followed separate careers. During French's time starring in Murder Most Horrid from 1991 to 1999, she played a different character each week, whether it was the murderer, victim or even both.

In 2002, French appeared in the comedy/drama mini-series Ted and Alice. The series was set in the Lake District where French played a tourist-information officer who incidentally falls in love with an alien.

She has also appeared in the BBC sitcom Wild West along with Catherine Tate, in which she played a woman living in Cornwall who is a lesbian more through lack of choice than any specific natural urge. This series was not met with as much success as her earlier role, ending after two years in 2004.

French's biggest solo television role to date has been as the title figure in the long running and popular BBC comedy The Vicar of Dibley, created by Richard Curtis. She starred as Geraldine Granger, a vicar of a small village called Dibley. In the final full-length episode of the well-known series, 12.3 million people watched the episode to see her character's marriage ceremony.

Her last appearance on The Vicar of Dibley was with Sting and Trudie Styler in a special mini episode made for Comic Relief in 2007. She was nominated for a BAFTA for "best comedy performance" in last episode of The Vicar of Dibley. Repeats of the show on BBC One still attract millions of viewers.