France smashed Switzerland 5-2 in Group E on Friday to take their World Cup tally to eight goals from two matches.
Giroud opened the scoring for Didier Deschamps' team and also notched an assist, while Benzema scored France's fourth goal and set up two others.
Benzema moved to three goals for the tournament, with the Real Madrid striker having scored seven goals in his past six matches for France, while Giroud - in his maiden World Cup start - struck his fourth goal in five games.
Against Switzerland, Deschamps picked Giroud as France's centre forward, while Benzema was moved to the left wing, forcing Antoine Griezmann to the bench, and the two strikers thrived.
Speaking to L'Equipe after the game, Giroud conceded he had never imagined France would start so strongly in Brazil.
"To be honest, no," the Arsenal striker said.
"We have produced eight goals that's very good. Well, we also conceded two at the end but do not deny our pleasure.
"It's very satisfying, it gives us great confidence for the future. We want to finish first...we must finish the job."
Benzema was named man of the match by FIFA for the second game in a row but claimed an improved team ethic has been key to France's success so far, rather than any individual performances.
France's World Cup campaign four years ago was plagued by infighting and player unrest, as they were eliminated in South Africa, after registering just one point and one goal in three games.
"We all played well, and we got off to a really good start, continuing where we left off against Honduras and playing as a team. And we really are a team," the 26-year-old said.
"There's no sulking; those that start the match and those that come on as subs put in the same level of effort. I feel great but we need to keep it up, as I can only perform well with the help of my team-mates."
Despite their two wins, France still need at least a point in their last group fixture against Ecuador to advance to the round of 16.
France claimed their only World Cup title in 1998 on home soil.
‘England have the players to win the World Cup – it’ll be tough for Thomas Tuchel to do a bad job, with the squad he has at his disposal’ Former Three Lions winger backs new boss after gentle qualifying draw
‘This is the hardest Manchester derby to call in years – Manchester United shouldn’t be petrified, it feels like Manchester City aren’t in control of any game at the moment’ Former Red Devils striker thinks a surprise result could be possible
