Da Mosto's family has been part of Venice's history since possibly as early as the fifth century. Originally, they were wine maker - the name da Mosto coming from the word "mosto" meaning grape must (juice from crushed grapes). Later, the family became traders, explorers and politicians.

The family's previous Venice residence, the Ca' da Mosto which can be seen from the Rialto market by the Grand Canal was lost through marriage in the 17th century, when a female member of the family married four times, with each husband dying of natural causes — thus enabling her to become one of the wealthiest people in Venice. Unfortunately for the da Mosto family, the childless widow had a falling out with them and left everything to a nephew of her second husband, who went on to become Doge.

Da Mosto is the younger son of Count Ranieri da Mosto and Contessa Maria Grazia Vanni d'Archirafi, who comes from a very old Sicilian Noble Family who are the Dukes of Archirafi and include many noted Italian diplomats and bankers. As the younger son of a count of the Venetian Republic Francesco is entitled to use the prefix Count before his name. A Roman Catholic, da Mosto took his first Holy Communion in the crypt of St Marks. A few years later, he received the sacrament of Confirmation from the future Pope John Paul I.

Da Mosto lives in his family home in Venice, with his South African born wife Jane, his three children, and his parents. Francesco’s grandfather, Andrea, acquired the palazzo where the family live in 1919. When he moved in, the empty picture frames on the walls of the portego were filled with copies of family pictures, including a 15th-century map of the voyages of Alvise da Mosto, who discovered the Cape Verde islands off the west of Africa.

When BBC Two decided to make a four-part series about the history of Venice, they contacted Francesco to be the host. He has now presented three series for BBC Two: Francesco's Venice, Francesco's Italy - from Top to Toe and Francesco's Mediterranean Voyage, with accompanying books to the series. He has also published a book entitled Francesco's Kitchen.

In the Doctor Who Confidential series 5 episode Death in Venice Francesco is featured explaining the history of Venice to Matt Smith.