It seems that the Seigneurial rights to Nègrepelisse and surrounding territory, passed from the hands of Carmain through marriage, to the St Suplice family, then to Beaumanoir (who in 1616 sold the Comté and the rights attached thereto, to Henri de la Tour, Duc de Bouillon) and to Montluc (Adrien Montluc had married Jeanne de Foix-Carmain).
If we go back in history, we see that the Carmains started out as the family Duèze, and Jacques Duèze became Pope (1316-34) as Jean XXII succeeding Clement V. The latter was Bernard de Goth from Bordeaux, and he was a friend of Philippe le Bel, who from 1307 gave hell to the Templars and their wealth to himself. Clement abolished the Order of Templars in 1312. Pope Jean’s brother, Pierre, was thus well placed to purchase Nègrepelisse and many Templar properties, as well as the Carmain estate from Bernard de Lautrec, and from that time the main branch of the family became Carmain de Nègrepelisse. I then found that Jean de Carmain in 1427 married Isabelle, the inheritor of Archambaud de Foix, with a stipulation that their descendants take the name and arms of Foix. Subsequently, in 1540 Louis de Foix-Carmain married Marguerite de Foix-Candalle.
The Balzac d’Espard arms include : or, 3 pals sable
The Foix arms are: or, 3 pals gules (but the original Grailly arms included a croix, sable)