John III of Armagnac was a count of Armagnac, of Fézensac and Rodez from 1384 to 1391.
He was the son of John II of Armagnac, and Jeanne of Périgord.
In 1390, John claimed the kingdom of Majorca, but was overcome by the troops of Juan I of Aragon, in a battle near Navata. John III consequently led military actions in Roussillon. On May 14, 1378, John III married Marguerite (1363–1443), countess of Comminges (1363–1443).
They had two daughters:
Jeanne, who married Guillaume-Amanieu de Madaillan (1375–1414) in 1409.
Marguerite who married Guillaume II, Viscount of Narbonne in 1415. He was killed in the battle of Verneuil, on August 14, 1424).