France increased their points total to 6 with the win and qualified for the second round, while Peru is eliminated after two defeats.
However, Peru was unable to find a way through and Ricardo Gareca's side - who have yet to find the net in Russian Federation - are certain to be knocked out.
However, France had the first real chances.
Peru, unfortunate to lose 1-0 to Denmark in their first game, took until the half-hour to have their first serious chance, with recalled skipper Paolo Guerrero stinging the legs of Hugo Lloris. He is quick, powerful, confident with both feet and was arguably one of the stand-out performers of the World Cup's opening round of matches, despite being on the losing side.
Gallese then blocked a right-footed drive from Antoine Griezmann after Giroud brought down an aerial ball from the deep in the 17th minute. France have an arguably incorrect VAR decision to thank for their victory, after taking the lead through a contentious penalty kick.
Pedro Aquino rattled the crossbar for Peru with a long shot in the second half but France were comfortable winners.
Peru's 4-2-3-1 formation is set up to provide Guerrero with as much service as possible from midfield, with Andre Carillo, Christian Cueva and Edison Flores all working to provide him the ball.
The Chelsea striker will be the focal point of Les Bleus attack in Ekateringburg, with Ousmane Dembélé dropping out.
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.
- France are unbeaten in their last eight World Cup fixtures against CONMEBOL opposition (W4 D4).
- Les Bleus have qualified for the knockout stages of the World Cup for the sixth time in their last eight appearances - only failing to do so in 2002 and 2010.
The Argentine acknowledged his players would probably be outgunned by France in every area of the pitch at the Ekaterinburg Arena.
Thursday marked the 100th worldwide appearance for Lloris.