VERSAILLES, July 6, 2013 (AFP) - The 32-year-old former US Open champion has dropped just three shots over 54 holes and could have held the lead outright were it not for a missed short putt on 17 that was a rare blemish to his immaculate short game.
Sterne meanwhile took advantage of a back nine collapse by Denmark's Thomas Bjorn and will pair McDowell for what should be a thrilling final round on Sunday at the sun kissed Le Golf National course outside Versailles, which will host the 2018 Ryder Cup.
"I played very nicely today, I really did. Sort of carried on from what I did on Thursday and Friday," said McDowell.
"This golf course demands fairways and greens, most golf courses do but this one even more so, shots offline get punished heavily here," said McDowell.
"You go into the rough here, you may not find your golf ball. You may lose your golf bag, that's how thick the rough is."
When asked about his growing confidence, he replied: "The last 10 or 11 holes there, I really started to feel it coming. I bogeyed 17 probably off the best tee shot I hit all day.
"All in all I'm really, really happy with the way I'm playing. Worked hard on my game and looking forward to the opportunity tomorrow."
Sterne opened his round brightly with two birdies on the first three holes but followed that up with bogey, double bogey, before steadying the ship and going on to drop just one more shot all day while picking up birdies at 14 and 17 to share the overnight lead.
Bjorn meanwhile had an inconsistent round that showed flashes of brilliance combined with missed opportunities that mirrored his second round when he fired five birdies and three bogeys.
The veteran Dane overcame a double bogey at the second hole before back to back birdies and then nearly drained a sensational hole-in-one at the par 3 eighth when his iron shot hit the pin but stayed out.
However, when he was locked in a tie for the lead with McDowell coming down the back nine, the wheels came off in spectacular fashion as he finished bogey, double bogey, par, bogey to drop to two-under for the tournament.
Austria's Bernd Wiesberger is nicely placed on four under along with Aussie Richard Green and Englishman David Howell.
Overnight leader Fabrizio Zanotti had a day to forget as the Paraguayan exploded with a seven-over par that included two triple bogeys in the first seven holes and leaves his dreams of a maiden European Tour victory all but ruined.
England's Simon Dyson and Denmark's Soren Kjeldsen are also in the hunt and two shots back on three under after rounds of 72 and 73 respectively while seven players are locked on two under, including Spaniard Jorge Campillo, who had the day's joint best score of 68.
Campillo had an almost flawless round with four birdies before his only bogey on 18 left him three shots adrift but gaining in confidence, heading into what should be a dramatic final round.
Ryder Cup hero Ian Poulter shot a solid round of two under 69 to sit par for the tournament while former world number one Luke Donald again failed to make an impact and is two over after a round of par-71
Leading scores after the third round in the French Open at Le Golf National outside Versailles on Saturday (GBR & IRL unless stated, par 71):
208 - Graeme McDowell 69-69-70, Richard Sterne (RSA) 68-69-71
209 - Bernd Wiesberger (AUT) 70-71-68, David Howell 69-71-69, Richard Green (AUS) 69-70-70
210 - Simon Dyson 70-68-72, Soren Kjeldsen (DEN) 69-68-73
211 - Thomas Bjorn (DEN) 68-69-74, Jorge Campillo (ESP) 74-69-68, Hennie Otto (RSA) 71-71-69, Lee Slattery 71-70-70, Marc Warren 69-72-70, Jamie Donaldson 70-70-71, Eduardo De La Riva (ESP) 72-67-72, Graeme Storm 70-68-73
212 - Francesco Molinari (ITA) 71-74-67, Simon Khan 71-73-68, Gregory Bourdy (FRA) 69-73-70
213 - Ignacio Garrido (ESP) 75-70-68, Miguel Angel Jimenez (ESP) 69-76-68, Ian Poulter 73-71-69, David Drysdale 70-74-69, Martin Kaymer (GER) 68-76-69, Chris Doak 71-70-72, Richie Ramsey 69-71-73, Stephen Gallacher 68-70-75
214 - John Parry 74-70-70, Ross Fisher 70-73-71, Rafa Cabrera-Bello (ESP) 70-72-72, Kristoffer Broberg (SWE) 72-69-73, Felipe Aguilar (CHI) 68-72-74, Fabrizio Zanotti (PAR) 68-68-78
215 - Luke Donald 71-73-71, Gareth Maybin 71-73-71, Robert-Jan Derksen (NED) 72-70-73, Scott Henry 73-68-74, Joost Luiten (NED) 71-71-73, Matteo Manassero (ITA) 73-69-73, Gareth Shaw 72-69-74, Matthew Nixon 68-73-74