Foucquet was born in Vezelay, Yonne, France, and entered the Society of Jesus in Paris in 1681. There he completed his studies for the priesthood and was ordained in 1693. The following year he volunteered for the missions in the East. Assigned to China, he arrived in Amoy (Xiamen) in 1699. Successful in developing mission stations in Fukien (Fujian) and Kiangsi (Jiangxi) Provinces, he was called to Peking (Beijing) in 1711 by the emperor; who wanted him to assist Joachim Bouvet in studying the I-ching (Book of changes). He was soon asked to explain principles of astronomy and mathematics.
Over the next seven years Foucquet wrote several essays on figurism, which aimed at finding the figures of the Old Testament in the Chinese classics. As part of this enterprise, he was perhaps the first Jesuit to cite Taoist literature. While in Canton, Foucquet had denied the common Jesuit position on the Chinese rites. He saw figurism as a way between that position and its opposing view, which understood the Chinese philosophers as atheists. Foucquet's refusal to accept a confrere as his superior led to his recall to France in 1720. Seeking to present his figurist ideas to the Holy See, he went to Rome, where he was consecrated a bishop in St. Peter's Basilica in 1725. In Paris he had become acquainted with Voltaire and the Duc de Saint-Simon, and in Rome Montesquieu had several discussions with him. Moreover, his correspondence helped several French scholars to develop sinology in France.
Having received Foucquet's letter containing some of his figurist views, a prelate in Canton wrote Propaganda Fide that these were contrary to sacred Scripture. In 1736 its investigation commission concurred, and the cause of figurism ended. A year after Foucquet's death the papacy condemned the Jesuit interpretation of the rites.