Here is the rough Google translation of Sotheby’s catalogue note: "Our picture is probably the double portrait of the second Mademoiselle de Blois and Mademoiselle de Nantes, the legitimized daughters of Louis XIV and the Marquise de Montespan.
Louise-Francoise de Bourbon, known as Mademoiselle de Nantes (1673-1743), Duchess of Bourbon and then Princess of Conde, had been legitimized by the Parliament in the year of her birth. Raised by Madame de Maintenon, she was married in 1685 to the Duke of Bourbon, grandson of the Grand Condé.
Francoise-Marie de Bourbon called the second Mademoiselle de Blois (1677-1749), was only legitimized in 1681. Louis XIV had indeed separated from the Marquise de Montespan under the pressure of the court in 1675, before To reconnect. Francoise-Marie and her brother, the Count of Toulouse, were therefore considered the fruits of a perjury. As a result, Madame de Maintenon refused to raise them with the other children born of this liaison. In 1692 Françoise-Marie married Philippe d'Orleans, future Regent.
For the Court, the marriage of "bastards" with princes of blood was a scandal. The two sisters had always maintained a hostile relationship, undermined by jealousy. Things became even worse when the Duc de Berry, the grandson of Louis XIV, married the daughter of Francoise-Marie d'Orleans in 1710. Louise-Francoise de Conde had coveted the Duc de Berry for her own daughter.”
From the Sotheby's Web site. Also posted to the End of the Era Album here.