Kim rolled in three birdies in her last eight holes in a three-under-par 68 to briefly claim the clubhouse at women's golf's fourth major of the year.
After holding a share of the first-round lead, the 24-year-old Sydney star found herself one shot behind South Korean pacesetter Somi Lee, who posted a second straight 66 to soar to 10 under.
"We were first off at seven so it was an early start, but I wanted to make sure I took advantage of that tee time. It's nice to be done before midday," Kim said.
"I just knew how much this course can really sting you, so I just played fairways and greens. Had a few putts more than yesterday but just kept it simple and it kind of worked out today."
Lee nabbed six birdies and an eagle in a superb second round to set a cracking pace at the postcard perfect Evian Resort Golf Club nestled between Lake Geneva and the Alps.
American first-round co-leader Jennifer Kupcho carded a 69 to be safely in the clubhouse at eight under, two shots behind the leader, with Hye-Jin Choi (68) three strokes back following the morning wave of finishers.
World No.1 Nelly Korda went round in 70 on Friday to edge to five under and stay well in the mix.
Gabriela Ruffels, one of the five first-round joint leaders at six under, was due to tee off among the afternoon starters.
So was fellow Australian Minjee Lee, two weeks after snaring a third career major at the Women's PGA Championship in Texas.
And after finishing runner-up last year, Kim's fellow Sydneysider Steph Kyriacou moved into contention again with a second-round 68 to climb to four under par through 36 holes.
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