Mouret was a great-nephew of the famous chess player Philidor. He learned the game at the Café de la Régence, taught by Bernard and Carlier, two of Philidor's students. He was a pupil of Alexandre Deschapelles and later he became a teacher of La Bourdonnais. He also gave chess lessons to the children of the French King Louis Philippe I. In 1819, he was the operator of The Turk during its tour in England and probably the person, who sold the secret of The Turk to the press.