He was born in Le Puy-en-Velay, Haute-Loire, Auvergne, where his father was a minor official. After a period as a professor of philosophy in the provinces, he was appointed a school inspector, thus obtaining a practical acquaintance with the needs of French education. In 1885 he was elected to the chamber as an Opportunist Republican. After acting as "reporter" of the budget for public instruction, he became minister for the department, in Alexandre Ribot's cabinet, in 1892. In April 1893 he formed a ministry himself, taking as his office that of minister of the interior, but resigned at the end of November, and on 5 December was elected president of the chamber. During his first week of office ananarchist, Vaillant, who had managed to gain admission to the chamber, threw a bomb at the president, and Dupuy's calm response -- "Messieurs, la séance continue" -- gained him much credit.

In May 1894 he again became premier and minister of the interior; and he was at President Carnot's side when Carnot was stabbed to death at Lyons in June. He then stood for the presidency, but was defeated, and his cabinet remained in office till January 1895; under this government, Alfred Dreyfus was arrested and condemned (23 December 1894). The progress of the Dreyfus Affair cast its shadow over Dupuy, along with other French "ministrables," but in November 1898, after Henri Brisson had at last remitted the case to the judgment of the court of cassation, he formed a cabinet of Republican concentration.

In view of the apparent likelihood that the judges of the criminal division of the court of cassation -- who formed the ordinary tribunal for such an appeal — would decide in favour of Dreyfus, it was thought that Dupuy's new cabinet would be strong enough to reconcile public opinion to such a result; but, to the surprise of outside observers, Dupuy proposed a law in the chamber transferring the decision to a full court of all the divisions of the court of cassation. This arbitrary act, though adopted by the chamber, was construed as a fresh attempt to maintain the judgment of the first court - martial. In the interim, President Félix Faure (an anti - Dreyfusard) died, and the accession of Émile Loubet helped placate the public. The whole court of cassation decided that there must be a new court - martial, and Dupuy at once resigned (June 1899). In June 1900 he was elected senator for the Haute Saône.

Although none of Dupuy's Presidential bids were successful, he served, due to his position as Prime Minister, as an Acting President of the French Republic for three separate occasions during vacancies.