Bickerton hit 10 fairways and 15 greens in regulation in the first round to complete a bogey-free 8-under-par 63 -- one shot off the course record at Le Golf National's Albatross Course.
New Zealand's Michael Campbell, the 2005 U.S. Open champion, opened with a 6-under 65 and stands alone in second place, one shot ahead of Swede Joakim Backstrom.
Backstrom was 8 under through 13 holes -- staring down the course record set by Eduardo Romero last year -- but he bogeyed three of his final four holes to drop to 5 under.
Sharing fourth place at minus-4 are Benn Barham, David Carter, Mark Foster and Oliver Whiteley of England; South Africa's Darren Fichardt; Jose Manuel Lara of Spain; and Sweden's Henrik Stenson.
Two-time defending champion Jean-Francois Remesy of France, who bested Jean Van de Velde in a playoff last year, leads a group of nine players tied for 11th place at 3 under.
Bickerton, last year's Abama Open de Canarias winner, wrestled free of some putting problems with an adjustment he made on the putting green recently.
Whatever he did worked on Thursday, as the 36-year-old needed just 25 putts to finish his first round.
'You just get a feeling,' said Bickerton, who lost a playoff to Niclas Fasth at the Andalucia Open in April.
Bickerton cashed in on that feeling with three birdies on his first nine holes -- the back nine -- and five more after that. He one-putted 11 times and two-putted seven times, finishing without a single three-putt green.
'It might be different tomorrow,' Bickerton said of his new putting stroke, 'but it made me feel good today and gave me one thought to work on and that is sometimes the key to playing well -- not having too much on your mind.'
Campbell also finished without a three-putt while using a new putter. The putter he ditched -- the one that helped him win at Pinehurst No. 2 -- had been with him for two years.
'It wasn't working,' admitted Campbell, who is currently ranked 45th on the Order of Merit. 'It is in my office right now. I'm sure it will be back, but right now it needs to be rested.'
Playing with Remesy and 2006 U.S. Open challenger Padraig Harrington, Campbell missed a short par putt at his first hole, the par-4 10th. But it was the only hiccup in an otherwise bogey-free round with his new putter.
'Today was a prime example of when the mind is free, things can come to fruition,' Campbell said.
Sharing 11th place with Remesy are Markus Brier, Paul Broadhurst, Andrew Coltart, Richard Finch, Peter Gustafsson, Soren Hansen, David Park and Ian Poulter.
Harrington and Van de Velde lead a group of 13 players knotted one stroke further back in 20th place at 2-under-par 69.
The French Open -- the oldest of the European continental Opens -- is celebrating its 100th anniversary.