The third-round co-leader along with Richard Sterne, McDowell took advantage of Sterne's struggles on the final day to finish well ahead of him at 9-under-par 275 at Le Golf National.
The Northern Irishman, who won the PGA Tour's RBC Heritage in April, posted his second European Tour triumph of the season.
Sterne stumbled to an even-par 71, ending in second place at 5-under 271.
Tying for third at at 4-under with matching 2-under 69s were Graeme Storm and Eduardo De la Riva.
Simon Dyson (71) corralled sole possession of fifth place at minus-3.