Englishmen Malcolm Mackenzie and Kenneth Ferrie finished one shot back after shooting 68s. Also in fourth place at 4-under were South Africa's Trevor Immelman, Stephen Gallacher of Scotland and Australia's Richard Green.
Ian Woosnam, Malaysian Open winner Alastair Forsyth and defending champion Jose Maria Olazabal were among 13 players tied for ninth with 3-under 69s.
The 30-year-old Olander played the back nine first and dug himself a huge hole with double-bogeys on the 11th and 12th holes. He battled back with a birdie at the 14th, then began his steady ascent up the leaderboard with an up-and-down birdie at the par-5 18th.
Birdies on holes 1 through 7 gave Olander an amazing eight in a row to equal a European Tour record. His birdie on the seventh came via a long chip-in, but he missed the green with his tee shot at the par-3 eighth and took a bogey.
Check out Olander's record-tying eight-straight birdies
Olander closed his eventful day with a birdie at the par-5 ninth.
'It was a strange round,' said Olander, who captured the Challenge Tour's Hardelot Challenge de France last year to earn his way back onto the European Tour. 'Quite a tough start. But I tried to stay positive because after three holes of a tournament you can't really conclude what will happen over the next four days. I told myself to focus even harder on each shot and hopefully some birdies will come. And they did.'
Olander became the ninth player in tour history to make eight birdies in succession. Woosnam and Seve Ballesteros each turned the trick in 1985, while 1998 British Open champion Mark O'Meara had his run of eight straight at the 1996 Alfred Dunhill Cup at St. Andrews. At the 1999 European Open at the K Club, Darren Clarke used a record-tying birdie streak to become the first player to shoot 60 twice on the European Tour.
Tony Johnstone, John Bickerton, Raymond Russell and Marcello Santi also share the record.
'I wasn't aware of the record,' Olander admitted. 'I wanted to make birdie on eight. But that is a tough hole. I tried to cut the three-iron into a back right pin and blocked it right. I tried to hole the chip but it ran 15 feet by and missed the putt. But it was still a nice run.'
Montgomerie, the 2000 winner at Le Golf National, was one-under through the 12th but finished with a flourish by birdieing four of the final six holes. The winner of seven straight Order of Merit titles is seeking his first top-10 result of the season.
'I spent about three hours on the range this morning working things out technically and took it on to the course,' he said. 'I played quite well. Six birdies, my only dropped shot was the ninth. It was the only green I missed.'
Check out Montgomerie's Scorecard
Remesy's scorecard was comprised of seven birdies and a double-bogey. With a victory this week, he would become the first Frenchman to win the Open de France since Jean Garaialde in 1969.
Olazabal, who survived a 36-hole final day to win last year's rain-plagued Open de France by two shots, is currently ranked third on both the European Order of Merit and the PGA Tour money list. He captured the Hong Kong Open at the start of the European Tour season and won the PGA Tour's Buick Invitational in February.
Full-field scores from the Novotel Perrier Open de France