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Gregorini was born in Rome, Italy, the daughter of former Bond girl Barbara Bach and businessman Augusto Gregorini. Her mother is of Jewish and Irish descent. She is also the stepdaughter of Beatles drummer Ringo Starr. In 1990 she graduated from Brown University.
Francesca has contributed two songs to the soundtrack of the minor film "See Jane Run" (2001), in which she also had a small acting role. She worked as a musician with her first c.d. “Sequel” (2003, where she sings, plays the guitar and the bass).
Gregorini sold scripts to both HBO and Paramount Pictures before co-helming, with Tatiana von Furstenberg, her directorial debut Tanner Hall, a coming of age story set in an all-girls boarding school in Rhode Island. Gregorini and von Furstenberg also co-wrote the independent film, which is loosely based on their own experiences during adolescence. Gregorini said in an interview, “Naturally there are some autobiographical elements, combined with things we'd witness in boarding school, and many other parts that we made up completely. You will certainly find characteristics of both of us in each of the 4 main girls and if you spend even a half hour with us, it will be very apparent to you, which girls are most like me and which ones are most like Tatiana.” The film was an official selection at the 2009 Toronto International Film Festival.
- Carlos N. (June 17, 2003). "Biography of Barbara Bach". barbara-bach.com. Retrieved 2006-11-24. "Biography has been written from information compiled by press interviews, books, newspaper articles and biographies."
- Gregorini interview
- . July 2002 http://perso.wanadoo.es/fgfanpage/2002.htm. Retrieved 23 February 2014. Missing or empty
- . July 2002 http://www.standard.co.uk/showbiz/ringos-girl-dumped-by-lesbian-7166992.html. Retrieved 23 February 2014. Missing or empty