Adelaide de Bourbon was spared by the revolutionaries because of her charitable works during the ancien régime. Her Wikipedia article is here.
Princess Adélaïde's coiffure and hat are late ancien régime, but her dress is glamorized Greek-inspired revolutionary style. Her hair is very, very long. She was probably in Spain, to where she had been exiled in 1797, when Vigée-Lebrun painted this portrait.
Keywords: 1800, Vigée-Lebrun, Princess, Bourbon family, Spanish, long frizzy coiffure, hat, scoop neckline, three quarter length close sleeves, jacket, buttons, belt, Empire low waistline, close skirt, earrings, jeweled belt buckle, tassels