VERSAILLES, July 5, 2014 (AFP) - The 34-year-old Reno, Nevada native, saw French playing partner Victor Riu pull within one shot with three birdies on the front nine before disaster struck for the 29-year-old local favourite.
Six bogeys down the stretch for Riu saw him slip into a tie for second with Thailand's Thongchai Jaidee on five under.
"I'm satisfied to finish these 18 holes, the score was pretty average today but nothing too terrible," said Stadler.
"I wasn't striking the ball as good as I have, but I picked up a lot of pars.
"It was difficult today with the wind, there were cross winds which made it tricky.
"I tweaked my back a while back and it hasn't been great for a couple of months but it wasn't too too painful, I'll get some treatment on it now.
"It will probably be more of the same tomorrow (Sunday), try to make a lot of pars."
Jaidee moved into contention with a fine round of two under par 69 that leaves him four back of Stadler while US Open champion Martin Kaymer carded 70 to stand alone in fourth, a further two shots back.
"The good thing today was my putting, except for the last hole where I made bogey," said Jaidee.
"It's going to be a very challenging day tomorrow (Sunday), it was windy today and raining at times, sometimes the wind was blowing in different directions and it was gusty which made it difficult," added Jaidee.
Stadler, the son of former Masters' winner Craig 'the Walrus' Stadler is making his first appearance at the Albatross layout near Versailles as he chases a third career victory.
After winning the Johnnie Walker Classic in 2006, he returned to winning ways in February at the Phoenix Open and is now set to play at the British Open on July 17 at Hoylake for the first time since 2008.
Riu, meanwhile, is having the best tournament of his career as the two men were followed by huge crowds despite chilly, wet weather that was sprinkled with sunny spells at the venue for the 2018 Ryder Cup.
The right hander from just down the road at Saint-Nom-la-Breteche, is on the verge of qualifying for his first major tournament at the Open and can do so by finishing in the top ten on Sunday.
"I'm a bit disappointed with my finish after a good start. I was a bit tired at the end but I'm happy to finish the 18 holes," said a slightly dejected Riu.
"I missed a couple of puts by just a few centimetres."
Riu is set to start his final round in the company of Kaymer in the penultimate group with Stadler and Jaidee going out last at 12h45 local time (1045 GMT).
"To play with Martin Kaymer will put a bit of pressure on me and I'm sure there will be a lot of people tomorrow but I'm looking forward to it," added Riu.
Englishman Matthew Baldwin and Austria's Bernd Wiesberger are tied for fifth on two under, while a group of five players including defending champion Graeme McDowell of Northern Ireland are a further shot adrift.
Sweden's Robert Karlsson, Irishman Damien McGrane, Michael Hoey of Northern Ireland and Englishman Mark Foster are all part of this group, chasing the three top ten places that will book a ticket to the British Open.
Leading scores after the third round of the EPGA French Open at the par-71 Le Golf National on Saturday:
204 - Kevin Stadler (USA) 64-68-72
208 - Victor Riu (FRA) 68-67-73, Thongchai Jaidee (THA) 70-69-69
210 - Martin Kaymer (GER) 72-68-70
211 - Matthew Badwin (ENG) 70-71-70, Bernd Wiesberger (AUT) 70-70-71
212 - Robert Karlsson (SWE) 73-69-70, Damien McGrane (IRL) 71-69-72, Michael Hoey (NIR) 73-66-73, Mark Foster (ENG) 69-70-73, Graeme McDowell (NIR) 70-69-73
213 - Scott Jamieson (SCO 69-70-74, Kiradech Aphibarnrat (THA) 77-66-70, Matthew Nixon (ENG) 71-72-70, Alexander Levy (FRA) 69-72-72, Julien Quesne (FRA) 74-71-68, Jamie Donaldson (WAL) 67-72-74, Stephen Gallacher (SCO) 66-73-74
214 - Matt Ford (ENG) 70-74-70, David Lynn (ENG) 73-69-72, Wade Ormsby (AUS) 70-75-69, Marcel Siem (GER) 65-72-77
215 - Magnus A Carlsson (SWE) 73-72-70, Mikko Korhonen (FIN) 72-72-71, Estanislao Goya (ARG) 75-66-74, Anders Hansen (DEN) 71-71-73, Roope Kakko (FIN) 68-74-73, Thomas Linard (FRA) 72-70-73, Joost Luiten (NED) 73-69-73, Marc Warren (SCO) 69-73-73