Feuvrier was born in Saulx, Haute-Saône to François Antoine, a military veterinary surgeon. In 1861–1865, he attended the Military School of Hygiene in Strasbourg, and earned a post-doc at Val-de-Grâce in Paris. Feuvrier served in Algeria (1861–1865) and Colmar (1869). He participated in the Franco-Prussian War.
Feuvrier then served as a personal physician to Prince Nicholas I of Montenegro (r. 1860–1918). He also participated under Nicholas I in the Herzegovina uprising (1875–1877) directed against the Ottoman Empire.
Feuvrier succeeded another Frenchman, Joseph Désiré Tholozan, as Naser al-Din Shah Qajar's personal physician. Though his knowledge of the Persian language and culture was limited (learned mainly on the spot), his travelogue provides invaluable first-hand information on an important period during the Qajar era. It is a major source of information in relation to the Tobacco Concession and the Tobacco Protest. Through his personal interest in Persian culture, Feuvrier's travelogue also provides important information on Iran's archaeology, architecture, urbanism, economy, and social life.
He was awarded the Order of the Lion and the Sun (1st class with green sash) and the Légion d’Honneur (chevalier, 1875; officier, 1890). In addition to his native French, and Persian, Feuvrier held linguistic abilities in Serbian, Italian, Russian, English, and German. He died at Saulx.