Benda was born in Benátky nad Jizerou, Bohemia. His parents were Jan Jiří Benda and Dorothea Benda. Jan Jiří was a weaver and an amateur musician. Dorothea Benda (née Brixi) was the daughter of a musician. He had four brothers, Johann Benda, Joseph Benda, Viktor Benda, and Georg Benda. Franz was the oldest surviving son. Three of his brothers became musicians. Viktor did not become a musician.