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I have found a source which details the names of the family members of Nicholas Tussa. There are a couple of options, but I believe the information may indicate that your mystery model's name may have been Anna. (see update)
Searching further within the same repository which holds your Levinger monograph on Trutat, the Bibliothèque Nationale de France, I find a legal notice published in the Journal de la Côte-d'Or on 24 march 1846 which concerns the Nicolas Tussa family from Dijon. The first paragraph of note mentions three minor children and the name of the wife, deceased by that date:
2° A M. Pierre Russet, ancien officier, demeurant à Dijon, en qualité de subrogé tuteur de Charlotte-Joséphine Tussa, Jean-Baptiste-Charles-Louis Tussa et Charles-Jean-Baptiste-Gustave Tussa, tous trois enfans mineurs issus du mariage de M. Nicolas Tussa, ancien libraire, demeurant à Dijon, avec dame Françoise Lambelin, son épouse, décédée;
Translation (emphasis mine):
2° To Mr. Pierre Russet, former officer, residing in Dijon, as subrogate tutor of Charlotte-Joséphine Tussa, Jean-Baptiste-Charles-Louis Tussa and Charles-Jean-Baptiste-Gustave Tussa, all three minors being children of the marriage of Mr. Nicolas Tussa, former bookseller, residing in Dijon, and Mrs. Françoise Lambelin, his wife, deceased;
So here you get the name of the wife and three children who are minors. The next several items list some adult Tussas; item 5 is of particular interest:
3° A M. Charles-Jean-Baptiste Tussa, majeur, domicilié à Dijon;
4° A Mlle. Marie-Louise Tussa, célibataire, majeure, demeurant à Dijon;
5° Et à Mlle. Anna-Françoise Tussa, demeurant à Paris, rue Hauteville, n° 89,
3° To Mr. Charles-Jean-Baptiste Tussa, adult, with a house in Dijon;
4° To Mlle. Marie-Louise Tussa, unmarried, adult, residing in Dijon;
5° And to Mlle. Anna-Françoise Tussa, residing in Paris, rue Hauteville, n° 89.
So we have an Anna-Françoise Tussa, living in Paris in 1846, within 2 years of the time of the painting. I believe this may be your model.
UPDATE
A general search of the parents names on the web brings up a genealogical page which has more information which draws a different conclusion. This page lists a daughter Louise Josephine as the likely candidate, with that individual dying on Martinique in 1850. (Unsourced genealogical material is often something I consider a hint when doing research; It can be valuable, but it has no real weight as proof until sources are found which confirm it)
Certain aspects of this match the information from the OPs original citation, and some doesn't fit the information from the source I cite above. Perhaps the Louise Josephine Tussa is actually the person listed as Marie Louise in the above source, but she was listed as living in Dijon at the time of the article, so we have no way of placing her with the painter in Paris. Dying in 1850 in Martinique however would match the loosing contact aspect after emigrating to America(the Carribean in this case).