Dubuisson, bidding to record the first home victory in the $3 million (2 million pound) event since Thomas Levet in 2011, shot a one-under 70 to share the lead with Ryder Cup team mate German Martin Kaymer (69) and Spain's Rafa Cabrera-Bello (70).
"I had a great round and I'm very happy about the way I played today," the Frenchman told reporters after finishing with a four-under tally of 138. "It was really tough out there with the wind this afternoon."
Paratore missed the cut despite making European Tour history by becoming the first player to reel off 18 straight fours in a round.
"It's strange," said the 18-year-old after his 72 gave him a total of 150.
"I took a photo of my scorecard and maybe I'll put it on Twitter later. You could say it was a solid round."
Ryder Cup pair Graeme McDowell, who was aiming to win the French Open for the third year in a row, and Lee Westwood also missed the cut.
(Writing by Tony Jimenez, editing by xxx)
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