Defending Olympic champion Xander Schauffele shares top spot at the halfway point at Le Golf National, with Rory McIlroy trailing the current Open and PGA champion by six shots.
However, McIlroy's team-mate Shane Lowry insisted he was now only "playing for pride" after recording a second successive round of 71.
Schauffele shot a five-under-par 66 in his second round to reach 11 under and draw level with overnight leader Hideki Matsuyama of Japan, who carded a 68.
Overnight storm showers kept the course soft and helped produce a flurry of birdies, with Britain's Tommy Fleetwood among those to shine, also reaching 11 under with a round of 64.
Spain's Jon Rahm is two shots behind the leaders in fourth, with Belgium's Thomas Detry, South Korea's Tom Kim and CT Pan of Chinese Taipei tied for fifth.
Speaking after his round, in-form Schauffele said: "If you do hit a bad shot it's easier to accept it because you know you're playing really good golf and you can make it up somewhere else."
The American found the rough along the 13th fairway and discovered that his ball was lying on an anthill and sought advice from tournament officials before hacking his way on towards a bogey.
"I've had burrowing animal issues but not like an ant pile that you can't really move," he said.
McIlroy's 69 saw him finish the day on five under, alongside Canada's Corey Conners and Jason Day of Australia.
The Holywood world number three registered an eagle and a birdie in his first five holes, but couldn't sustain his bright start, recording jus two more birdies as well as two bogeys and a double bogey.
McIlroy said: "The birdies are out there, I know that, so if I can tidy up a couple of things I can try get myself back up that leader board and in contention for a medal."
Lowry, who is level for the tournament and back in a share of 43rd was left lamenting putting woes in a round which featured two birdies and as many bogeys.
"Today was pretty similar to yesterday, he told RTÉ Sport. "I never really got anything going. It was a bit of a boring round.
"Disappointing, but what can you do? I tried my hardest, but it wasn't good enough. I gave myself a lot of chances but the putter was cold and the leaders are flying away with it, so I’ve probably given myself too much to do.
"I’m playing for pride this weekend now, and I’ll go away this afternoon and reflect on the last couple of days and give it a good go at the weekend and try to get myself as far up the leaderboard as I can."
Riffing on his putting issues, the Offaly man added: "I kept hitting it inside 20 feet all day and never really holed anything. I was burning the edge as well and the frustrating thing is that I felt like I was hitting good putts, I was just struggling to read the greens.
"But that’s golf, that’s just the way it is and unfortunately, it’s happened the last two days for me."
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