Cugnot was born in Paris, son of the sculptor Etienne Cugnot. He entered the École nationale supérieure des Beaux-Arts in the 1850s under teachers Francisque Joseph Duret and Georges Diebolt. Cugnot took the Prix de Rome in 1859 along with co-winner Alexandre Falguière, and was a pensioner of the Villa Medici in Rome from 1860 to 1863.
In 1874 he was made a Knight of the Legion of Honor.
Napoleon seated on an eagle dominating the world, plaster, at the Musée d'Orsay, 1869
the 1871 tomb of Generals Jacques Léon Clément-Thomas and Claude Lecomte, two of the first casualties of the Paris Commune, in the 4th division of Père Lachaise Cemetery in Paris, with architect Ernest Coquart
Monument to the Battle of Callao, with a finial figure of Nike, historical and allegorical bronzes, and friezes of the battle, for Plaza Dos de Mayo, Lima, Peru, circa 1873
interior allegorical figures of Paving and Gas for the Palais Garnier, Paris, circa 1874
pediment figures of Justice and Strength in the Court of Cassation, Paris, circa 1879
