The son of Antoine Boizot, a designer at the Gobelins tapestry manufacture, Boizot worked in the atelier of sculptor René-Michel Slodtz (1705–1764), who also trained Houdon. Boizot married Marguerite Virginie Guibert, the daughter of sculptor Honoré Guibert. In 1778 he was admitted to the Académie royale de peinture et de sculpture and exhibited at the yearly salons until 1800. His portrait busts of Louis XVI and Joseph II were created in 1777 and made in bisque porcelain at Sèvres.
From 1773 to 1800 Boizot directed the sculpture workshop of the Sèvres porcelain Manufactory, producing the series of unglazed biscuit figures with a matte finish resembling that of marble.
Boizot also created terracotta designs for gilt-bronze clock cases, such as that of the allegorical “Avignon” clock in the Wallace Collection in London, which was cast and chased by Pierre Gouthière in 1777.