As a boy, Franchetti studied composition and piano with his father, the Baron Alberto Franchetti (1860–1942). Baron Franchetti was a wealthy, well-respected and successful composer of the operas often performed at La Scala including Germania (performed by Enrico Caruso, conducted by Arturo Toscanini) and Christoforo Colombo. Urban legend has it that Luigi Illica's libretto of Tosca was first offered to Franchetti who, too busy at the time with other projects, passed it on to his friend Puccini.
Arnold Franchetti studied physics at the University of Florence, music at the Salzburg Mozarteum, and then moved to Munich from 1937 to 1939, where he studied composition and orchestration with composer Richard Strauss. After a brief stint with the Italian army during World War II, Franchetti joined the anti-Mussolini underground resistance in the Italian Alps where he helped Allied airmen escape.