The American world number one secured his seventh win of the year with a course record-equalling 62 at Le Golf National to edge out silver medallist Fleetwood on 19-under par for the tournament.
Japan's Hideki Matsuyama had to settle for bronze on 17 under after a dramatic final round that saw several players challenge for the medals.
Jon Rahm sat four shots ahead after 10 holes but fell away badly to finish tied fifth with Rory McIlroy, whose hopes were dashed by a double-bogey on the 15th.
"I did it myself. What it represents and what it could have been for Spain is what makes it more painful," said Rahm.
Reigning champion Xander Schauffele, who was tied for the overnight lead with Rahm, dropped out of contention with a three-over back nine.
"It sucks. Not very happy with it to be honest," said the PGA Championship and British Open champion. "Not a whole lot of positives, obviously, from it."
Frenchman Victor Perez delighted the home fans with a stunning surge through the field but finished in fourth place despite his 63, which included a run of four birdies and an eagle in the space of five holes.
Scheffler continued his magnificent season, which has also delivered his second Masters and Players Championship titles, with a majestic fourth round.
He was six strokes off the pace at one point during the back nine, but carded a six-under 29 for the inward half as those behind him on the course, especially Rahm, faltered.
Rahm blows lead
Rahm had eased into a four-shot lead with six birdies in his first 10 holes and appeared to be cruising to the title.
But back-to-back bogeys, coupled with successive birdies from Fleetwood, saw the Spaniard's advantage evaporate.
Scheffler, McIlroy, Matsuyama and Perez all seized the opportunity to charge into contention, leaving the top six players on the leaderboard separated by just two shots as the final group headed into the last five holes.
Ireland's McIlroy was the first to blink, dumping his approach shot on the 15th hole into the water to all but end his title tilt.
Rahm then suffered another serious dent to his bid when he contrived to make a double-bogey on the easy par-five 14th.
Perez narrowly missed long birdie putts on the final two greens but set the clubhouse target at 16-under overall after a sparkling back-nine 29 which sent roars echoing across the Albatros course.
Scheffler, who had earlier started the day with three straight birdies, moved into the solo lead for the first time with a fourth successive birdie on the 17th, despite having found the rough off the tee.
He safely parred the last to set a mark of 19-under, which Fleetwood reached with a brilliant birdie on the 16th.
But the Englishman handed a shot back on the 17th after a clumsy chip from just off the green, leaving himself needing birdie at the last to force a play-off.
Fleetwood could not produce any more late heroics to suffer yet another near-miss in his career, while Scheffler celebrated on the practice range.
