Françoise was the daughter of René I de Rohan and Isabel d'Albret of Navarre.
Through her father, Françoise was descended from 11th-15th century Breton dukes, while on her mother's side she was a niece of Henry d'Albret, King of Navarre, who had married Marguerite d'Angoulême.
Her aunt, Queen Marguerite, had Françoise educated with her own daughter, Jeanne, the future mother of Henry IV.
[2] Françoise and her best friend Catherine de Parthenay, who was her sister-in-law by marriage to René II de Rohan, acted as the benefactors and protectors of the French mathematician François Viète between 1572 and 1591.
He dedicated them his most famous work on new algebra, In artem analyticem isagoge (fr).