House of La Tour d'Auvergne
She married twice; firstly to Louis Charles de La Tour d'Auvergne, styled the "prince de Turenne" and son and heir of Godefroy Maurice de La Tour d'Auvergne and one of the famous Mazarinettes, Marie Anne Mancini. The couple married in Paris on 16 February 1691. As the House of La Tour d'Auvergne ranked as Foreign princes at Versailles, this entitled them to the style of "Highness". As such, Anne Geneviève took on this style.