The eighth seed, who claimed a career-boosting title at the Miami Open this year, will play her second Grand Slam last-eight match against another American, Madison Keys.
The 14th-seeded Keys experienced little trouble in a 6-2 6-4 victory against Czech Katerina Siniakova.
"I just wanted to enjoy myself here, play with freedom," said Barty, who also reached the last eight at the Australian Open this year.
Barty rushed to a 5-1 lead, wrapping up the opening set on serve after Kenin briefly threatened a comeback by pulling a break back.
The American had found her range, though, and she went 3-0 up in the second, pulling her opponent around the court -- just as she did in beating 23-time Grand Slam champion Serena Williams in the previous round.
She saved two break points at 5-3 and levelled the tie at the third attempt when Barty fluffed a forehand.
But she had nothing left in the tank in the decider, being fed a bagel that put a brutal end to her Paris run.
On Court Suzanne Lenglen, Keys was always in control against world number 42 Siniakova, advancing smoothly in light drizzle.
After easing into a one-set lead Keys, a semi-finalist here last year, encountered some resistance from Siniakova, who however bowed out on her serve when she sent a forehand long.
(Reporting by Julien Pretot; Editing by Tony Lawrence)
