Nilsson produced his fantastic round at Le Golf National course – the venue for the 2018 Ryder Cup – despite not having a top 35 finish all season.
He holds a one shot lead over Gary Boyd, Matteo Manassero and Thongchai Jaidee.
"It's been a struggle for me so far this year. My long game was pretty bad, but it's improved and this is good for my confidence," said Nilsson.
Amongst the big names at the event are Lee Westwood (70), Justin Rose (71) and Graeme McDowell (72) who all remain in the mix despite unspectacular rounds.
However, it was another miserable day for former world number three Paul Casey who shot a nine-over round of 80 as he struggles to recover from the dislocated shoulder he suffered snowboarding late last year.