Gonshaw’s father came to England as a child with his parents as Russian White emigres fleeing from the Bolshevik Revolution. Francesca Gonshaw was born in Marylebone, London in 1959, and attended St Paul’s Girls’ School. The family relocated from London to Marbella, Spain in 1976. At the age of 17 she returned to England to study for her A Levels in Cambridge. She also studied acting, but did not complete the course, and was a model in a photo story for My Guy magazine..

Gonshaw began her television acting career in the early 1980s. In 1982 she appeared in a BBC television play entitled Shades. The following year, she was in Gesualdo The Prince, based on the true story of Carlo Gesualdo who murdered his wife and her lover after discovering them in bed together.

In 1982, Gonshaw played Kate in You Should See Us Now by Peter Tinniswood, at the Greenwich Theatre. the cast also included Simon Cadell, Christopher Cazenove and Pauline Yates.

She played Arsinoe in the 1983 BBC television classical Roman history drama series The Cleopatras. That same year, she had a role in The Hound of the Baskervilles (1983). From 1984 to 1985, she was the character Lisa Walters in the Central soap-opera Crossroads. In February 1984, Hilary Kingsley of The Daily Mirror criticised Gonshaw’s performance in Crossroads, saying that she “[spoke] her lines as though reading them from an optician’s chart.”

From 1984 to 1986, she appeared as waitress Maria Recamier in the BBC’s ‘Allo ‘Allo! television situation comedy series set in occupied France during World War II. The producers had wanted to cast Mary Stävin, but the Department of Employment refused permission, saying that they believed a British actress could be found for the role, and Gonshaw was given the part. The show satirised dramas such as Secret Army, and like other UK situation comedies of the time, contained double entendres, catchphrases, and running gags. Critics complained that the show was “sexist, racist, homophobic and, like [producer David] Croft’s earlier Dad’s Army, trivialised war”. It ran for 85 episodes from 1982 to 1992, attracting as many as 17 million viewers per episode in the UK, and was sold to overseas markets including France and Germany. Gonshaw was in 21 of the episodes, in the first three series. She complained in a 1986 interview that “I wanted to be a serious actress. Now I seem to be known only as a bawdy waitress wearing stockings and suspenders.” Gonshaw left the cast of ‘Allo ‘Allo after its third series to take up the role of Amanda Parker in the third series of the BBC television drama series Howards’ Way in 1987. She also started attending the Byam Shaw School of Art, studying painting.

In the mid-1980s she joined the New Shakespeare Company’s tour of thirteen countries in the Middle East, portraying Hermia in A Midsummer Night’s Dream. She was in a production of The Cat and the Canary in 1988. The Stage’s Eric Harris saw her nearly trip over in the performance that he watched, writing “perhaps it was divine retribution for the daft way was she was playing the young female lead – all clear eyes and simpers like a panto’s principal girl.”

In 1990 Gonshaw played Ophelia in Hamlet, at the Brixton Assembly Rooms, Pentameters in Hampstead, and the Shaw Theatre. The title role was played by Mr S Haynes, who had been sentenced to 11 years’ imprisonment in France for dealing in heroin, but then pardoned by President Mitterrand. Having promised to do something positive with his life if pardoned, Haynes decided that he would stage Hamlet. The production was helped by Trevor Nunn and Sir John Gielgud. Timothy West provided his voice to play the Ghost. Haynes had AIDS, and the proceeds of the performances were to benefit AIDS charities. Helen Gould, reviewing the production in The Stage, said that Gonshaw as Ophelia was “a whining rag doll given to declamatory gestures.”

In 1992, she appeared in the pop music video for the Peter Gabriel single release “Digging in the Dirt” Also she appeared in the official video of Moonlight Shadow by Mike Oldfield.

Gonshaw retired from acting in the early 1990s, and took up the post of Senior Vice-President of Creative Affairs with Miramax Books & Films. In 2001 she was a casting agent for the film The Goose Creek Story. From 2009 she has been an artist, and was the curator of the ‘She has a Space’ gallery in London. She exhibited at the 7–8 October 2009 Art for Youth event at the Mall Galleries. Since 2011 she has occasionally appeared at memorabilia collectors conventions with the former cast of Allo Allo