Born in Paris, Questel was a student of Félix Duban at the École nationale supérieure des Beaux-Arts, and took a second-place Prix de Rome in 1844. He became a member of the Académie des Beaux-Arts in 1871.
Questel became the patron of his own atelier at the Ecole. Among his students were Henri Paul Nénot, Ernest Sanson, and the Swiss architect Alfred Friedrich Bluntschli; he was the father-in-law of French architect Honoré Daumet.
Questel died in Paris. Upon his death the atelier was taken over by Jean-Louis Pascal.
His architectural work includes:
- the church of Saint-Paul in Nîmes built from 1835 through 1849
- restoration of the Roman aqueduct Pont du Gard, Vers-Pont-du-Gard, southern France, 1841-1846
- the Pradier Fountain, Nîmes, 1851
- the Saint Anne Hospital in Paris, 1867
- Préfecture de l'Isère, Grenoble, 1861-1866
- the Library and Museum of Grenoble, 1872
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