François-Henri Clicquot (1732 - 1790) was a French organ builder.

He was grandson of Robert Clicquot and son of Louis-Alexandre Cliquot, who were also noted organ builders. François-Henri inherited his father's workshop.

He reconstructed the organ of St. Gervais in 1758, and built the organs at St. Sulpice, St. Nicolas-des-Champs, Souvigny, and at Poitiers Cathedral.