Marie-Antoinette and the Carmelites

Tea at Trianon offers insight into the order's connections with the French Royal Family:

The French court was shaken in 1674 when Louise de la Vallière, the former mistress of Louis XIV, publicly begged the queen's forgiveness and entered a Carmelite monastery. In his book To Quell the Terror, William Bush details the many connections of the later Bourbons with Carmel, particularly the patronage of Queen Marie Lesczynska and her daughter Madame Louise. When Louise herself chose to become a Carmelite nun in 1770, it cemented the spiritual ties between those in the worldliness of Versailles and those in the austerity of the cloister.

Marie-Antoinette of Austria married the Dauphin in the same year that Madame Louise entered the monastery. The young princess offered to represent Louis XV at the ceremony at which his daughter Louise received the habit of Carmel, since it was too painful for the king and the rest of his family to be present. So it was the teenaged Marie-Antoinette who veiled the new "Soeur Thérèse de Saint-Augustin."
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It was at the request of Madame Louise, however, that Marie-Antoinette granted a dowry to a poor, pious girl named Mademoiselle Lidoine, so that she could enter the Carmel of Compiègne. Mademoiselle Lidoine became the Mother Prioress of the heroic Martyrs of Compiègne, who like Marie-Antoinette, died on the guillotine during the French Revolution.