In 1832–34 and 1838–39 he was active as an opera composer in Naples, with some of his works premiering under the name "Carlo Coen". In 1841 his opera Antonio Foscarini premiered successfully at the Teatro Comunale di Bologna, prompting a revival the following year at the Teatro Regio di Torino. He was thereafter active as music teacher in Paris, including teaching at the Conservatoire de Paris, and was for a time director of the conservatory in Lille.
Cohen's opera "l'Impératrice", was performed around 1834 in Naples, Paris, and London. Moreover, he published four tracts about musical theory. On his advice as singing tutor, Marguerite Baux made her début in February 1876 as Rachel in La Juive, although initially she had been expected to sing Marguerite in Gounod's Faust.
Cohen published several works on numismatics during his lifetime. His Guide de l'amateur des livres à vignettes du XVIII Siècle went through four editions and is considered the standard bibliography of French 18th century illustrated books. He is perhaps best known for his two fundamental works on ancient numismatics: the first, published in 1854, dealt with the Roman Republican coinage, while the second, issued in eight volumes from 1859 to 1868, focused on the coinage of the Roman Empire, from Pompey to Romulus Augustus (49 B.C. - 476). Cohen was also curator of the numismatics collection at the Bibliothèque nationale de France in Paris.
- Faust and Marguerite, opera, Paris 1846
- Description générale de monnaies de la république romaine (Paris, 1854)
- Guide de l'acheteur de médailles romaines et byzantines (Paris, 1876)
- Description historique des Monnaies frappées sous l'Empire romain, communément appelées Médailles impériales, 8 vols (Paris, 1859–1868)
- Guide de l'amateur de livres à vignettes du XVIII-e siècle (Paris, 1870; reprints: 1873, 1877, 1880)
- Casaglia, Gherardo (2005). "Henri Cohen". L'Almanacco di Gherardo Casaglia (in Italian).
- "Biographies de numismates: Henry Cohen (1806-1880)". SacraMoneta. Archived from the original on 1 January 2011. Retrieved 14 January 2009..
- "Marguerite Baux" (in French). Association l'Art Lyrique Français. Retrieved 10 June 2019.
- The Musical World. J. Alfredo Novello. 1876. pp. 124–.
- "Henry Cohen's Work". VirtulCohen.com. Retrieved 14 January 2009..
- Opera News, vol. 18, p. 6 (1953).