Cornet, ranked 37, took advantage of an error-strewn performance from the Polish world number one to win 6-4, 6-2 on Court One in their third-round tie.
Swiatek was broken five times and made a total of 33 unforced errors in an uncharacteristically sloppy display.
The 21-year-old, who had won her previous six tournaments including the French Open, said she struggled to control the ball.
"I know I didn't play good tennis," said the world number one. "I was pretty confused about my tactics.
"As a solid player, she used that pretty well. For sure, it wasn't a good performance from me."
Swiatek had not lost a match since her defeat to Jelena Ostapenko in February in Dubai.
Though she had looked unbeatable on hard courts and clay, she had admitted she was on a learning curve on grass.
She was made to battle hard in the second round to defeat lucky loser Lesley Pattinama Kerkhove in three sets and has yet to beat a top-50 player on grass.
Swiatek said she had not felt in her best shape at Wimbledon during practice despite her stellar form this season.
"I'm kind of aware that this could happen," she said. "Maybe it's not the right attitude to have, but it is like it is.
"I tried many things to feel better on a grass court but it didn't really work out.
"That's why I'm not even hard on myself because, like, it's kind of logic that if I couldn't find it even in practice, I'm not going to find it in a match."
In reaching the fourth round, Cornet matches her run at Wimbledon in 2014, when she beat Serena Williams in the third round.
"I have no words right now," she said. "It reminds me of the time I beat Serena on the same court eight years ago exactly. This court is a lucky charm for me."
The 32-year-old reached a career milestone by defeating former number one Simona Halep to advance to her first major quarter-final at the Australian Open earlier this year.
"I'm like good wine," said Cornet, who is contesting her 62nd consecutive Slam, matching Ai Sugiyama's record.
"In France good wine always ages well, that's what's happened to me. It's unreal -- I'm playing one of the best seasons of my career."
Cornet will face Australia's Ajla Tomljanovic for a place in the quarter-finals.
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