McDowell battled to a 1-under 70 in Saturday's round and Sterne completed the circuit at Le Golf National at even-par, but it was enough to claim a 1-stroke lead over the trio of Bernd Wiesberger, David Howell and Richard Green.
McDowell, who won the Volvo Match Play Championship this year, said Le Golf National was a formidable venue.
"This course demands fairways and greens; most courses do but this one even more so," he said. "Shots off line here get punished heavily and the greens are very firm."
McDowell had a quiet round, with two birdies and a bogey on the 17th hole. Sterne had two bogeys and a double-bogey, but birdied 14 and 17 to move to the head of the pack with McDowell.
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