Desgots was the nephew of, and assistant to, Andre le Notre (died 1700). He visited England on Le Notre's behalf in 1689 concerning a proposed garden at Greenwich Park, London, England which never materialized.
Desgots himself designed two English gardens. In 1700 he designed the Maestricht garden at Windsor Castle and around 1713 he designed parterres for the Earl of Orkney at Cliveden.
Upon le Notre's death in 1700 Desgots suceeded him as controleur general des batiments. He designed and redesigned several European gardens after that including perhaps most notably the gardens of the Luxembourg and Palais Royal.
Desgots died in 1732.
Woodbridge, Kenneth, "Desgots, Claude", The Oxford Companion to Gardens, ed. Geoffrey and Susan Jellicoe et. al. (Oxford: Oxford University Press, 1991), p. 139