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.
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