Unheralded Swiss player Morgane Metraux took the halfway lead at Le Golf National after a spectacular front-nine of 28 in a six-under-par 66, taking her to eight-under for the tournament.
China's Yin Ruoning is just one stroke behind after a bogey-free 65, while overnight leader Celine Boutier fell back with a four-over 76.
Korda is six shots adrift in a tie for 12th place after falling apart on the par-three 16th hole, when she looked poised to challenge for the lead.
The American hit her tee shot into the lake protecting the green before dumping her effort from the drop zone into a bunker.
Her shot from the sand, where her ball had plugged, flew way over the pin to the back of the green and she three-putted from there to card a ruinous seven.
"Those bunkers are really firm and when I tried to be a little aggressive with it, my ball just shot to the back of the green," Korda said.
"Just a series of unfortunate events happened in a row."
Korda won six LPGA Tour titles in the space of seven events earlier this season before suffering a dramatic loss of form with three successive missed cuts.
The first of those came at the US Women's Open, where she made a 10 on a par-three hole.
Korda has plenty of work to do to defend the crown she won in Tokyo despite finishing with her seventh birdie of the day for a two-under 70.
"I still have 36 more holes and anything can happen. I'm trying to see the positive in this," she said.
New Zealander Ko, the only golfer to win multiple Olympic individual medals, boosted her hopes of completing the set with a 67 to reach five-under overall, putting her in third place.
Former world number one Ko won silver in Rio eight years ago and took the bronze at the Tokyo Games.
She could have been even closer to Metraux's lead, but bogeyed the par-five 18th after hitting her third shot into the greenside bunker.
"Today I playing really solid and really didn't put myself in that many awkward positions," said Ko.
Metraux, ranked 137th in the world, took advantage of benign early conditions, making two eagles and four birdies in a sensational opening nine holes.
The gloss was taken off her score as she hit two shots into the water on the inward half, including on the 18th, although both times she limited the damage to bogeys.
Boutier slips back
Home favourite Boutier endured a miserable back nine to drop into the chasing pack.
Last year's Evian Championship winner started the day three shots clear at the top of the leaderboard but her second round unravelled when she hit her approach shot on the 13th into the water and made double-bogey.
Boutier compounded that error with a sloppy bogey on the par-five 14th and then found the water again on 15 en route to another double.
"Emotionally it was fine," she said when asked if the backing of the thousands of French fans following her had had an adverse effect on her game.
"Definitely feel like I left a few shots out there."
Boutier dropped into a tie for sixth on three-under.
South Africa's Ashleigh Buhai, the Philippines' Bianca Pagdanganan, Thai star Atthaya Thitikul, Japan's Miyu Yamashita and Yin's Chinese teammate Lin Xiyu are also just five strokes off the lead.
Slovenian Pia Babnik, the world number 341, and Mariajo Uribe of Colombia are a shot closer to the top three, tied for fourth.
