Davioud was born in Paris and studied at the École des Beaux-Arts under Léon Vaudoyer. After winning a Second Grand Prix de Rome, he was named inspector general for architectural works in Paris, and chief architect for its parks and public spaces.
As a colleague of the urban planner Baron Haussmann, he designed much of the characteristic Parisian street furniture: benches, pavilions, bandstands, fountains, lampposts, signposts, fences and balustrades, jetties, monuments, as well as a number of landmark buildings.
Among his most notable works are the popular Saint-Michel Fountain in Place Saint-Michel, the old Palais du Trocadéro (demolished 1937), and the two theatres at the Place du Châtelet (the Théâtre du Châtelet and the Théâtre de la Ville.)
In 1868, Davioud succeeded Jacques Landry as mayor of Houlgate, where he stayed until 1871. His mandate was interrupted when he was appointed capitaine du génie during the Franco-Prussian War. Noted for his work in Paris, he built a single villa in Houlgate, La Brise, on the Route de Caumont.
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- Le Panorama National, now the Théâtre du Rond-Point, created for the Universal Exposition of 1855
- Fontaine Saint-Michel, in the Place Saint-Michel, with sculptor Henri Alfred Jacquemart, 1860
- Two theatres at the Place du Châtelet (Théâtre du Châtelet and Théâtre de la Ville), 1860–1862
- Temple de la Sybille on the Île du Belvédère, Parc des Buttes-Chaumont, in the 19th arrondissement, 1869
- Fontaine de l'Observatoire and the Avenue de l'Observatoire (with sculptor Jean-Baptiste Carpeaux and others), 1873
- The Mairie, the municipal building in the 19th arrondissement, 1876–1878
- The former Palais du Trocadéro, built for the Universal Exposition of 1878
- Magasins-Réunis, in the Place de la République
- Jardin des Champs-Élysées
- Wrought-iron grillwork at the Parc Monceau
- Fontaine du Château d'eau, Place Daumesnil, 12th arrondissement
- Entry pavilions for the Bois de Boulogne, 16th arrondissement
- Square des Batignolles, 17th arrondissement
(See also Fountains in Paris)