It was not the complete display that Deschamps might have wished for, but with two wins from two matches, France are safely into the knockout rounds.
Peru are with zero points, while Denmark are second with four points.
Kylian Mbappe became France's youngest-ever World Cup goal scorer at the age of 19 as his strike secured the 1-0 win that put France through to the round-of-16 and sent an unlucky Peru side out. France is the third team during the World Cup that have qualified for the 1/8 finals, after Russians and Uruguayans.
Coach Didier Deschamps responded testily "there's always an opponent" when asked by reporters about France's failure to dominate and also about the strong pressure the Peruvians exerted in the second half.
"Peru were aggressive, as we expected them to be", the Tottenham Hotspur keeper told journalists in the mixed zone at Central Stadium.
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Shortly after the 10-minute mark France came close twice in quick succession, Griezmann firing wide from just inside the box and then Paul Pogba narrowly off target with a fierce angled effort.
In the first half, in particular, he was imperious, with the only notable blemish a 20-second lapse in which he gifted the ball away twice and threatened to allow his standards to drop.
With two wins from two matches in Group C, France is through to the next round with a match to spare.
Antoine Griezmann drove straight at goalkeeper Pedro Gallese after Olivier Giroud - starting in place of Ousmane Dembele - set up the Atletico Madrid forward.
However, the pace and quick passing of France meant they could turn it on at any moment.
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Cole had similarly kind words, calling him an "enormous talent" and saying he had a "strong desire to be a better person". He was arrested in December 2017 on charges that he beat up his pregnant girlfriend and later released on house arrest.
If Australia are to beat Denmark, they will have to find a way of breaching a defence that has kept five successive clean sheets and last conceded a goal 534 minutes ago. Following a through ball from Pogba, Giroud's left-footed drive from the left side of the box deflected past defender Christian Ramos, beating Gallese, who moved towards the right post.
France is leading Group C with 6 points.
Peru's fans could have had even more to cheer, were it not for several near misses.
Peru nearly got their equaliser when a 30-yard piledriver from Pedro Aquino flew inches away from the left post.
Jefferson Farfan hit the side netting with 17 minutes left as Ricardo Gareca's side began to run out of time to save their World Cup dream. France managed to hold to their slim advantage as Peru lacked quality in finishing.
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