The Northern Irishman, who has been struggling for form all year, added a second round of 78 to his opening 72 and at eight over par he had no chance of making the cut for the weekend.
In an uncustomarily scrappy round, on one of his favourite courses, McDowell had three bogeys and two double-bogeys.
He had been bidding to become just the second golfer to win three straight French Open titles after Marcel Dallemagne in 1938, one year before the outbreak of World War II.
He also would have been just the sixth golfer to have landed a a hat-trick of European Tour titles in the same event alongside Ian Woosnam, Nick Faldo, Colin Montgomerie, Tiger Woods and Ernie Els.