Raised at Besançon and trained at first by his father, he was apprenticed to a sculptor at Dijon, then developed his style during a decade in Paris in the studio of Pierre Le Gros the Elder (ca. 1677-87), before returning to his home region, where commissions for religious works on a small scale took him to Besançon and Poligny.
By about 1690 he was in Rome, where there was an established, tightly-knit community of Burgundian artists. Monnot was influenced by Domenico Guidi, to the extent that scholars have debated the attribution between Guidi and Monnot of the Burghley House Andromeda. Guidi, a pupil of Alessandro Algardi, had become a prominent Roman sculptor with Bernini's death in 1680. Monnot's first major commission was for two marble reliefs, a Nativity and a Flight into Egypt flanking Guidi's Dream of St. Joseph for the right transept altar in Santa Maria della Vittoria.
Monnot quickly intregrated into Rome's artistic circles and gained many commissions. With the award of the Saint Ignatius altar in the Church of the Gesù, to Le Gros the Younger in 1695, French sculptors in Rome became highly prized for decades to come. He was among the select group who were commissioned to provide apostles of heroic scale for niches in the Basilica of Saint John Lateran.
Commissions arrived from the English visitor, the Earl of Exeter, and above all from Kassel, where Monnot was responsible for the tour de force of white marble sculptures and bas-reliefs set against richly-colored marble revetments of the Marmorbad (the "Marble Bath") in the Karlsaue, Kassel, which is considered his masterwork. Monnot went to Kassel in 1714, and began by executing marble portrait busts of Karl, Landgrave of Hesse-Kassel (or Hesse-Cassel), and the Landgrafin. In January 1715 the first contracts were signed concerning the new Appartement du Bain with its statuary, ten sculptures that were already completed in Rome, some of them as early as 1692, and commissioned four white marble high relief panels for the outerwalls of the pavilion, eight further relief panels for the vaulting and the portrait medalion of Karl himself. Monnot established a studio with assistants in Kassel and to help him produce the works. Renewed agreements in 1718 increased the marble relief panels to the eight that were installed, and the ensemble was inaugurated in 1729. The final two statues, Minerva and Aurora, were announced as ready by Monnot in 1731, but did not actually reach Kassel until 1734.
The architect of the garden pavilion is unknown; Monnot's mythological sculptures occupy niches in the massive central pier, and his eight large white marble high relief panels of subjects from Ovid's Metamorphoses fill the piers between arch-headed windows.
Like all sculptors working in Rome, Monnot was called upon to restore fragmentary antiquities. Baroque restorations often took broader liberties of interpretation than eighteenth-century and later tastes permitted. Monnot restored a torso of a copy after Myron's Discobolus as a Wounded Gladiator who supports himself on his arm as he sinks to the ground; it was donated before 1734 by Pope Clement XII to the Capitoline Museums, where it remains. One of his pupils, Bartolomeo Cavaceppi (1716-1799), was a sculptor best known as a restorer of antiquities.