All I can find out about her is that she married in 1777.
Dorotheum's English language note follows, "Anne Catherine Le Preudhomme de Chatenoy married Jean Jacques Marie, Comte de Verdun in 1777, a rich member of the influential circle of the Comte d’Artois, brother of King Louis XVI. In her account book Madame Vigée Lebrun noted several portraits of her friend, painted in 1776, 1779, 1780 and 1782. The later ones are probably autograph replicas of the original painting, executed in 1776 which has as yet to be identified. It is probable that our painting is one of the later versions and was painted in 1780 or 1782. Some unimportant parts of the painting could have been executed by a collaborator in Vigée Lebrun´s studio as was usual practice from 1780 onwards, as the artist was very busy. Some of the most famous works of Vigée Lebrun are autograph replicas, for example, her famous self-portrait in the National Gallery, London, is a replica after the primary version in a Swiss private collection.
Mme Vigée Lebrun used here a very informal looking straw hat in the present painting that she used in several other portraits. She used it in 1781 in the portrait of the Comtesse Dubarry, mistress of the late King Louis XV. The artist herself is wearing the straw hat in her self-portrait of 1782. Later she painted the Princesse de Polignac and even Queen Marie Antoinette in her most famous informal portrait with a similar straw hat. She had probably been inspired by Rubens’s portrait of a “Lady with a straw hat” which she had seen in Brussels. Madame Élisabeth, sister of King Louis XVI., has been portrayed by Vigée-Lebrun in a nearly identical dress in 1782.
With this portrait of Madame de Verdun, a missing work by Élisabeth Vigee-Lebrun has been rediscovered."
From FA2010's collection on Wikimedia.