I cannot find information about who she is, but she is not Mlle. Caroline Rivière made famous by Ingres. However, she could be the Madame Rivière, née Marie-Françoise-Jacquette-Bibiane Blot de Beauregard, also portrayed by Ingres.
From Réunion des Musées Nationaux. Also posted to the Reign of Louis XVI - 1775 to 1789 Album here.
The bodice without revers or robings and coiffure with massive curls suggests this portrait dates to the erly- to middle-1780s.
Keywords: Heinsius, de la Rivière family, long bouffant coiffure, fur cape, lining, chemise, fitted bodice, full sleeves, notched jeweled arm bands, theatrical dress