The defending champion moved up the leader board on Friday as he hit four birdies and two bogeys to add a 69 to his opening 70 in Paris.
Kevin Stadler is out in front on 10 under and McDowell was quick to acknowledge another superb performance from the American.
The Portrush man, who won last year on nine under, said: "I said to (playing partner) Martin Kaymer it was nearly as good as his at Pinehurst, but not quite. It's a great display of golf.
"It's Kevin's type of golf course and if he keeps playing like that he's going to be tough to catch, but I feel like three under is not a bad return for the last two days and if I can go low tomorrow and get myself back into it, who knows?"
Michael Hoey was also on three under after Friday's round.