A philosophy professor before his election to the Chamber of Deputies (1885) from the Haute-Loire département, Dupuy joined Jules Ferry's moderate republicans. He served as minister of education from December 1892 to April 1893; he then formed his own government in April 1893 but resigned at the end of November and on December 5 was elected president of the Chamber. During his first week of office the anarchist Auguste Vaillant threw a bomb at him, and Dupuy's calm words, “The debate continues, gentlemen,” won him much credit. He became premier and minister of the interior in May 1894 and was by Pres. Sadi Carnot's side when the latter was assassinated at Lyon in June.

His Cabinet remained in office until January 1895, and it was under it that Capt. Alfred Dreyfus (Dreyfus, Alfred) (q.v.) was arrested and, two months later, condemned (December 1894). In November 1898, and after the Dreyfus case had at last been remitted to the judgment of the Supreme Court of Appeal, Dupuy formed a government of republican concentration. A special law was passed that transferred the decision from the criminal section to the Court of Appeal sitting as a whole (toutes chambres réunies). The latter decided that there must be a new court-martial, for the bordereau, the document that had led to Dreyfus' court-martial, was the work of Maj. F.W. Esterhazy. This infuriated the anti-Dreyfusards, who staged demonstrations and insulted Pres. Émile Loubet at Auteuil. Dupuy resigned on June 12, 1899. From June 1900 until his death he was senator for Haute-Loire.