Anne-Aymone is a great-niece of the Cuban-born French designer and architect José Emilio Terry y Dorticos and the aunt of Roger Marie Joseph Henri Sauvage de Brantes, the present Marquis de Brantes.

Through her mother she is a great-great-granddaughter of Cuban business magnate Tomás Terry y Adán.

The couple lived in her family home for the early years of their marriage, before settling at the rue Bénouville in the 16th arrondissement of Paris.

As First Lady of France, Anne-Aymone set up the Fondation pour l’Enfance in 1977 to raise awareness of child abuse.

[5] In December 2022, Anne-Aymone Giscard d'Estaing put up some of her and her late husband's art and furniture for sale at Hotel Drouot as she planned to move to a smaller Paris home.