Cherki replaced PSG forward Ousmane Dembele with six minutes remaining at Philadelphia Stadium in front of 68,324 fans.
Kylian Mbappe’s second-half penalty was the difference in an ill-tempered contest.
France struggled to break down a resolute Paraguay in the first half, Gustavo Alfaro’s side having already dumped Germany out of the competition at the Round of 32 stage.
But the two-time World Cup winners from 1998 and 2018 weren’t to be denied and got the breakthrough they needed.
Desire Doue was fouled inside the box by Brighton’s Diego Gomez and Real Madrid forward Mbappe took the penalty, sending Orlando Gill the wrong way to ensure progress for Didier Deschamps side.
Played in extreme heat conditions, Mbappe drew level with Argentina’s Lionel Messi on seven goals in the tournament’s Golden Boot race.
Mbappe now has 19 World Cup goals from 19 games as he chases Messi who boasts the record on 20.
France now face Morocco in the competition’s last eight on Thursday 9 July at Boston Stadium in Foxborough with kick-off at 21:00 (UK).
City Magazine: World Cup special available now!
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