I cannot find out who she was.
From mynewsdesk.com/se/stockholms_auktionsverk/images/3040-a-roslin-portrait-presume-de-mlle-de-fontenay-903396; spots and cracks removed with Photoshop. Also posted to the Reign of Louis XVI -1775 to 1789 Album here.
The Google translation of the caption is, "Mademoiselle de Fontenay, dressed in deep turquoise dress in silk, lace collar, lace cuffs and pink satin ribbon.”
Keywords: 1784, Roslin, Fontenay family, bouffant coiffure, floral ribbon headdress, lace scarf, bows, lace-trimmed fichu, bodice, elbow length upper sleeves, lace-trimmed flared cuffs