Cornet, ranked 37, took advantage of an error-strewn performance from her Polish opponent to win 6-4, 6-2 on Court No.1 in their third-round tie.
The top seed was on the back foot right from the start of the match, broken in her first two service games, and could not get back on level terms.
The 20-year-old broke at her first opportunity in the second set but the 32-year-old Cornet broke back immediately, repeating the feat twice more as Swiatek's game fell apart.
Swiatek made a total of 33 unforced errors in an uncharacteristically sloppy display. She had not lost a match since her defeat to Jelena Ostapenko in February at Dubai, winning her past six tournaments, including the French Open.
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