John III of Armagnac (1359 – July 25, 1391) 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.
In 1391, he had to leave for Italy in order to go to the assistance of Charles Visconti, Lord of Parma and husband of his sister, Beatrix of Armagnac. Visconti was in conflict with his acquisitive cousin Gian Galeazzo Visconti, later the duke of Milan, whose ambition was to control the whole of northern Italy.
His army was attacked and decisively beaten by that of Gian Galeazzo Visconti as it passed through Alessandria in Piedmont. John III was killed in the battle.
On May 14, 1378, John III married Marguerite (1363–1443), countess of Comminges (1363–1443). They had two daughters: