His brother Giovanni (1779 – 1851) was a prominent astronomer and Catholic priest.
As a young man, Francesco fought in the Napoleonic wars in 1799.
He then returned to Tuscany, where he began collecting mainly Etruscan antiquities.
He published illustrations of some of his collections in his ten volume Monumenti etruschi (1820–1827), Galleria Omerica (also titled Raccolta di monumenti antichi esibita dal cav.
Francesco Inghirami per servire allo studio dell'Illiade e dell'Odissea 3 volumes, 1829–1851), Pitture di vasi fittili (1831-1837), Museo etrusco chiusino (2 volumes, 1833), and the incomplete Storia della Toscana (1841-1845).