Darren Fichardt, who held the first-round lead, vaulted out of the gate with back-to-back birdies from the first as the wind let up somewhat at Le Golf National. The South African struggled from that point forward, however, to finish alone in fourth place at 3-under-par 139 after a round of 73.
Remesy, who can become the first Frenchman to win this event since Jean Garaialde titled in 1969, stumbled out of the gate with a bogey at the 10th, his first, but came right back with a birdie at the par-three 11th.
'It's a difficult golf course compared to last year,' said Remesy, who missed the cut at this event in 2003. 'You have to keep the ball on the fairway.'
The 40-year-old then birdied the par-four 15th and moved to minus-four with a birdie at the par-4 17th.
At the par-5 third, Remesy left his second shot in the greenside rough but chipped his third to the edge of the cup, just missing out an eagle. Remesy tapped in for birdie and drained an 18-footer for a birdie at the very next hole for his share of first.
'Now I have to continue to play my game and see what is going on,' said Remesy. 'The most important thing for me is to be in contention on Sunday afternoon with nine holes to play. I am not thinking about winning at the moment. There is one more round tomorrow and another one on Sunday so I have just made half of it.'
Woosnam, who is seeking his first stroke-play victory on the European Tour since the 1997 Volvo PGA Championship, knocked his second to six feet for a birdie at the first and added birdies at the fifth and the ninth to take the lead at 7-under.
The Welshman played his approach to five feet for a birdie at the 10th and ran home a long birdie putt at the 12th to stretch his advantage to three strokes.
Woosnam found trouble down the stretch with three consecutive bogeys starting at the par-4 15th to fall back into a tie with Remesy. He managed a par on the 18th to complete a round of 69.
'I'm disappointed with the finish but I would have taken joint leader at the beginning before I went out,' said Woosnam. 'For 14 holes I played some of the best golf I have played for a long time.'
Peter O'Malley and John Bickerton posted matching rounds of 67 to join David Howell in a tie for fifth at 2-under-par 140. Ian Poulter, Nick O'Hern and Mark Roe followed at 1-under-par 141.
The 36-hole cut fell at 7-over-par 149 with 74 players surviving for the weekend. Colin Montgomerie benefited from the high cut, after a second-round 75 placed him on the number.
Last year's champion Philip Golding could not recover from his disappointing opening round. Golding carded a 75 to finish at 16-over-par 158.