Jones, the overnight leader, carded a 5-under 67 in the third round. The leaders are two strokes clear of Hee-Won Han (65) and three ahead of Sophie Gustafson, who shot a third-round 67.
Inkster had a tremendous start to her round. She holed out from the fairway on No. 1 for an eagle to move to minus-8 for the tournament and followed that up with an eight-foot birdie putt at the third.
'I hit a really good drive and only had 67 yards to the pin,' said Inkster of her first hole. 'I hit it on the backstop, three yards past the hump and it rolled back off the hump and into the hole. That was a nice start.'
Trouble came calling on the par-4 fifth, however. She drove the ball in the right rough and had to pitch out. Inkster was unable to get up-and-down and that led to her bogeying No. 5 for the second straight round.
She erased that mistake by posting back-to-back birdies from the eighth to make the turn at 10-under.
Around the turn, Inkster continued her climb to the top of the leaderboard with birdies at 11 and 13. She continued her solid play on the 16th hole, which she birdied for the third consecutive round.
The 2002 U.S. Women's Open winner closed out her round with her third birdie of the tournament on the 18th hole.
'I played very well, drove it well, hit my irons well and putted well so I'm happy with the way I played today,' said Inkster. 'It was good to come back with a solid round today after yesterday and I know I will have to play well again tomorrow to win - I'd certainly take another 64.'
Jones began the day with a one-stoke lead at Royal Evian Golf Club. She quickly extended her advantage by birdieing the first two holes to get to minus-11. However, she stumbled to a bogey at the fifth, where she missed the fairway and her second shot came up short.
The 43-year-old again converted back-to-back birdies, this time from the eighth to head to the back nine at 12-under.
On the back side, Jones rolled in a three-foot birdie putt on 14. She joined Inkster atop the leaderboard with a birdie on No. 18, which she has also birdied all three rounds.
'I just tried to keep up with the group ahead of me, shooting 7- and 8-under,' said Jones. 'I knew there were some hot rounds out there. Any of these players are capable of that, and it didn't surprise me at all that Juli and Hee-Won did it because they've both been playing very well lately.'
Lorena Ochoa fell from second place to fifth after a round of 1-under 71. She completed 54 holes at 9-under-par 207 and is one stroke ahead of Se Ri Pak, Karrie Webb and Janice Moodie.
Michele Redman carded a 5-under 67 Friday to move to 7-under-par 209. She shares ninth place with Candie Kung and Cristie Kerr. Natalie Gulbis, Suzann Pettersen and Helen Alfredsson are one stroke further back at minus-6x.
Annika Sorenstam, the 2002 champion, moved from a tie for 34th to 18th place after a third-round, 5-under 67. She stands at 4-under-par 212.