She was a daughter of the great Wagnerian tenor Giuseppe Borgatti (1871–1950), whose imposing career at Milan's La Scala opera house was ended by blindness.
[1] Trained initially as a ballerina, she abandoned dance to become a concert pianist, specialising in the works of Claude Debussy.
A lesbian, she settled on the Mediterranean island of Capri in the early 1900s, where her lifestyle raised fewer eyebrows than elsewhere in Europe.
The duo remained together for just over a year, until Franchetti left Capri and was linked with the prominent American artist Romaine Brooks.
She also began a romantic liaison with Brooks, who was by that time pursuing a relationship with the American writer Natalie Barney.