He was the son of a bricklayer, David Mozart (1621–1685). Franz worked as a master mason and lived in the Fuggerei since 1681. He was born in Augsburg and died there. A commemorative plaque at his house there, Mittlere Gasse Nr. 14, commemorates him today. The bookbinder Johann Georg Mozart was his son.
Franz Mozart is not to be confused with Franz Xaver Wolfgang Mozart, the youngest son of Wolfgang Amadeus Mozart.
- Die Mozartstadt Augsburg: „die vatterstadt meines papa“, regio-augsburg.de (German).