He was born in Paris. His father, Professor Jean Louis Burnouf (1775-1844), was a classical scholar of high reputation, and the author, among other works, of an excellent translation of Tacitus (6 vols., 1827-1833). Eugène Burnouf published in 1826 an Essai sur le Pali ..., written in collaboration with Christian Lassen; and in the following year Observations grammaticales sur quelques passages de l'essai sur le Pali.
The next great work he undertook was the deciphering of the Avesta manuscripts brought to France by Anquetil-Duperron. By his research a knowledge of the Avestan language was first brought into the scientific world of Europe. He caused the Vendidad Sade, to be lithographed with the utmost care from the manuscript in the Bibliothèque Nationale, and published it in folio parts, 1829-1843.
From 1833 to 1835 he published his Commentaire sur le Yaçna, l'un des livres liturgiques des Parses; he also published the Sanskrit text and French translation of the Bhagavata Purana ou histoire poétique de Krichna in three folio volumes (1840-1847). His last works were Introduction à l'histoire du Bouddhisme indien (1844), and a translation of Le lotus de la bonne loi (The Lotus Sutra, 1852). He had been for twenty years a member of the Academie des Inscriptions and professor of Sanskrit in the Collège de France.
See a notice of Burnouf's works by Barthélemy Saint-Hilaire, prefixed to the second edition (1876) of the Introd. à l'histoire du Bouddhisme indien; also Naudet, Notice historique sur MM. Burnouf, père et fils, in Mém. de l'Acad. des Inscriptions, xx. A list of his valuable contributions to the Journal asiatique and of his manuscript writings, is given in the appendix to the Choix de lettres d'Eugène Burnouf (1891).