The National Gallery's notes for this follow, "The suggested identification of the sitter was given in the title in a 1907 sale catalogue. The sitter could be either Renée-Marguerite or Marie-Josèphe, daughters of Pierre-Louis, Marquis du Cambout, or Mlle du Cambout-Coislin, daughter of Pierre-Armand du Cambout (who married in 1727). This was probably painted in the 1750s."
From bbc.co.
I wonder if this portrait comes from the 1750s based on her dress that could be from a Rigaud portrait with vee neckline and sleeves flaring at least around the upper arms. The coiffure is also earlier 1700s post-Fontanges period.
Keywords: Liotard, Mademoiselle de Coslin, French, long straight coiffure, floral headdress, trapezoidal neckline, chemise, lace, vee neckline, upper flared long sleeves, floral bodice ornament, wrap