McGrane began the round with an eagle on the 10th hole at the Golf du Palais Royal course, followed by two birdies and two bogeys, but regrouped with back-to-back birdies on Nos. 17 and 18.
He ended the round with a birdie on the ninth hole for a two-stroke lead.
"I played beautifully today and I'm delighted with it," McGrane said. "I got off to a fast start and I managed to keep it going and finish it off nicely."
Alejandro Canizares is in second place with a five-under 67, and Edoardo Molinari was in a group of seven, including Richie Ramsay, Graeme Storm, Robert-Jan Derksen, Kenneth Ferrie, Phillip Rice and Jorge Campillo, tied for third at four-under 68.