Boichot studied with the sculptor Simon Challes and left for Italy in 1765, at his own expense. There he copied Antiques for English tourists. Boichot was particularly attracted by mannerist artists: Perino del Vaga, Daniele da Volterra and, in Fontainebleau, Primaticcio and Nicolo dell'Abate. He participated in many building projects during the Revolution and the Empire: he sculpted reliefs for the column of the Place Vendôme, for the Arc de Triomphe of the Carrousel and for the Pantheon. He exhibited at the Salon from 1789 to 1812. Drawings by him are in the Louvre, Besançon and in Châlon-sur-Saône, Paris, Grand Palais, Néoclassicisme français, Dessins des Musées de Province, 1974, nos. 8-10, illustrated.
A drawing by Boichot was offered at Christie's, Monaco, 2 July 1993, lot 79, illustrated.