Son of Mario and Flaminia Tucci, he was educated by his uncle Niccolò Tucci, Latin teacher and poet. He studied at the medicine and philosophy department at the university of Pisa, graduating with D. Vigna in 1629. He had an epistolary relationship with Galileo, who was admired by him.
In Lucca, he had a brilliant medical and naturalistic career distinguishing himself in the fight against the arise of the plague in 1630, when he sustained, in front of the Republic's General Council, the benefit of a sanitary set of rules and being able to stem the epidemic.
He was generously rewarded by the government of Lucca for his services.
He maintained a constant correspondence with F. Redi, M. Malpighi and with the anatomic C. Auber and G.A. Musner, he hosted in Lucca the danish doctor N. Stenone.
From his anatomical observations on dead bodies, he contributed to the acquired knowledge of the lymphatic vessels.
Fiorentini cultivated historical erudite interests, receiving the task, from Rome, to do some researches on the rich and unexplored archives of Lucca on Marilde of Canossa.
The work originated by the researches, “Memorie della gran contessa Matilde”, dedicated to pope Urbano VIII, was one of the first modern contributions on the knowledge of the medieval history, known and praised by G.W. von Leibnitz and L.A. Muratori.