Les Bleus prevailed thanks to a Kylian Mbappe first-half goal but Peru dominated and could have levelled after the break when Pedro Aquino's fierce strike hit the post.
Didier Deschamps' side, however, were aggressive in midfield, with Paul Pogba raising his level and the remarkable N'Golo Kante winning 13 tackles, after already winning the ball 14 times in the opening Group C game against Australia.
The 19-year-old Mbappe, now the youngest scorer for France at a World Cup, took the man-of-the-match award but Deschamps disagreed, praising midfielder Kante for another top-notch performance at the Ekaterinburg Arena.
"Kante had a great match. He was free in the system we chose, said Deschamps, referring to France's 4-2-3-1 formation after fielding a 4-3-3 in their 2-1 win against Australia.
"I don't vote for the man of the match. (Antoine) Griezmann was decisive, for example. Kante is not interested in the man of the match award."
Deschamps will be pleased that his team pressed their opponents throughout, which they failed to do against the Socceroos, triggering criticism from the coach.
Mbappe scored from Olivier Giroud's deflected shot, which came after Pogba had won the ball close to the Peru area.
"We matched them physically and it's a good sign," said midfielder Blaise Matuidi, who started the game after being benched against Australia.
France's defence was praiseworthy, solid from the onset, even if fullback Lucas Hernandez sometimes struggled on his left flank.
"France are a hard team to harness, they are extremely versatile and quick," said Peru coach Ricardo Gareca.
"Unlike in other matches, they played with flexibility and tactical discipline to neutralise Peru. They corrected their style over the course of the game.
"France did some outstanding work in defence. We did not fall short. That was my impression. They were well structured."
Les Bleus, who qualified for the knockout stage for the second consecutive time -- a first since 1986 -- next face Denmark, where they might want to polish their attacking style.
"Obviously with two wins we can win or draw and still be number one. But we will try to win. Would never think of finishing second," said Deschamps.
(Writing by Julien Pretot; Editing by Ian Chadband)
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