Damiron was born at Belleville. At nineteen he entered the normal school, where he studied under Eugène Burnouf, Abel-Francois Villemain, and Victor Cousin. After teaching for several years in provincial towns, he came to Paris, where he lectured on philosophy in various institutions, and finally became professor in the normal school, and titular professor at the Sorbonne. In 1824 he joined Paul-François Dubois and Théodore Simon Jouffroy in establishing the Globe; and he was also a member of the committee of the society which took for its motto Aide-toi, le ciel t'aidera. In 1833 he was appointed chevalier of the Legion of Honour, and in 1836 member of the Academy of Moral Sciences. Damiron died in Paris.
His chief works, of which the best are his accounts of French philosophers, are the following: An edition of the Nouveaux mélanges philosophiques de Jouffroy (1842), with a notice of the author, in which Damiron softened and omitted several expressions used by Jouffroy, which were opposed to the system of education adopted by the Sorbonne, an article which gave rise to a bitter controversy, and to a book by Pierre Leroux, De la mutilation des manuscrits de M. Jouffroy (1843); Essai sur l'histoire de la philosophie en France au XIX' siècle (I828, 3rd ed. 1834); Essai sur l'histoire de la philosophie en France au XVII' siècle (1846); Mémoires a servir pour l'histoire de la philosophie en France au XVIII' siècle (1858-1864); Cours de la philosophie; De la Providence (1849, 1850).