Fleetwood, who is hoping to emulate 2016 champion Justin Rose by winning gold for Great Britain, built impressively on his opening 67 with an eagle and three birdies in an outward nine of 31.
Further birdies followed on the 13th, 16th and 17th but the world number 14 was unable to save par at the last after an errant tee shot.
Fleetwood has shone at Le Golf National before, winning the 2017 French Open before claiming four points alongside Francesco Molinari at the 2018 Ryder Cup.
Great Britain’s Matt Fitzpatrick also shot his way back into the mix as the 2022 US Open champion rebounded from an opening 73 to match Fleetwood’s 64 and sit alongside McIlroy on five under.
McIlroy, who missed out on a bronze medal in a play-off on his Olympic debut in Tokyo, started strongly with an eagle and a birdie in his first five holes.
But his next birdie, on the ninth, was sandwiched between two dropped shots and he was made to wait until the 16th before picking up another shot.
The four-time major winner found trouble with his drive on the 17th, leading to a costly double bogey, before a superb approach at the last set up a closing birdie.
World number one Scottie Scheffler is at six under while McIlroy’s Team Ireland team-mate Shane Lowry’s second straight 71 left him on level par.