The French Open champion made seven birdies mixed with three bogeys on the Golf du Palais Royal course to move to a 12-under total of 132. Mikko Ilonen (66) of Finland and 2011 winner David Horsey (67) of Britain were tied for second.
The 72nd-ranked Siem needs to enter the top 50 by Sunday to earn his first invitation to the Masters from April 11-14. Pablo Larrazabal moved into contention with a 64 to sit four shots behind Siem.
"I think it should have been better than it was to be honest," Siem said. "The bogeys on four and seven were a bit weird because I was in the middle of the fairway there. I should accept the 68 because it's always nice to go under par after such a low round the day before, because that can be quite difficult to follow up on sometimes."
The 72nd-ranked Siem needs to enter the top 50 by Sunday to earn his first invitation to the Masters from April 11-14.
"I am trying my best. It is a tournament I have always wanted to play and if I can keep calm and play the way that I have been for the first two days here then I have a chance," he said, adding that the blustery conditions over the first two days have been to his liking. "I actually hope the wind blows a little bit more because I actually enjoy the challenge of playing into the wind, and it would also keep the guys behind me away from me, because if there is no wind out there then people can go very low around this course.
Pablo Larrazabal moved into contention with a 64 to sit four shots behind Siem. Alvaro Velasco of Spain was second overnight but dropped down the leaderboard after an erratic 74, to sit nine shots back.