She was born Marie Alice Heine at 900 Rue Royale, New Orleans, Louisiana. Her German Jewish father, Michel Heine, was a scion of a prominent Berlin and Paris banking family and a nephew of poet Heinrich Heine. He had emigrated from Germany to Paris in 1840, moved to New Orleans in 1843, and become a successful financier and real-estate developer. Her mother was Amelie Miltenberger, an architect's daughter, whose family had built three interconnected Miltenberger mansions on rue Royale.
The American Civil War sent the family back to France, where the teenage Alice's youth and beauty, and her family's wealth, made a great impression in Parisian society. A & M Heine, her father's firm, helped finance Napoleon’s war with Prussia.
Alice married her first husband, Marie Odet Armand Chapelle, Marquis of Jumilhac, 7th Duke of Richelieu, on February 27, 1875. Their only child, Armand, became the 8th and last Duke of Richelieu on the death of his father on June 28, 1880.
She converted from Judaism to Catholicism when she became the duchess of Richelieu. Marcel Proust used Alice as a model for the princesse de Luxembourg in À la recherche du temps perdu.
Alice's second marriage, to Prince Albert I of Monaco (as his second wife) occurred on October 30, 1889. The prince, whose first wife was a daughter of a Scottish duke, was an oceanographer and during his long journeys at sea, Alice took great interest in the Monegasque opera season. She became a lover of the composer Isidore de Lara, which resulted in Prince Albert striking her in view of an audience at the Salle Garnier. They separated judicially on May 30, 1902 (Monaco) and June 3, 1902 (France), but remained married.