Anne was born in Paris, France, the only daughter of Prince René of Bourbon-Parma and Princess Margaret of Denmark. Anne was the younger sister of Prince Jacques of Bourbon-Parma and elder sister to Prince Michel of Bourbon-Parma who married Princess Maria Pia of Savoy (eldest child of King Umberto II of Italy and Queen Marie José), and Prince André of Bourbon-Parma. As a granddaughter of Robert I, Duke of Parma she was first cousin to: King Boris III of Bulgaria; Robert Hugo, Duke of Parma; Princess Alicia, Dowager Duchess of Calabria; Carlos Hugo, Duke of Parma; Crown Prince Otto of Austria; and Grand Duke Jean of Luxembourg.