France is on the verge of qualifying for a European Championship quarterfinal, but Benzema has failed to shine.
Although he played his part in the 2-0 win against Ukraine, setting up Yohan Cabaye's goal with an exquisite turn and pass, more was expected of the Real Madrid striker heading into the tournament after he scored 21 league goals to help the club team to the Spanish title.
France can finish top of Group D if it beats Sweden in Kyiv on Tuesday, and Blanc is tipping Benzema to play a starring role.
"He can score at any time. Maybe if we hadn't taken him off (in the second half against Ukraine) he would have scored, and he will most probably score in the next game," France coach Laurent Blanc said. "The most important thing is that we're creating chances, no matter who scores."
Blanc has a point, because France won the 1998 World Cup without a goal from its centre forward, Stephane Guivarc'h, and with players chipping in from midfield and defence.
France's other goal against Ukraine on Friday was scored by winger Jeremy Menez, with Benzema also involved in the build up.
But the 24-year-old Benzema's total of 15 goals in 47 international appearances is lower than it should be, given his ability.
He has three goals in the past 14 games for France and never scored at a tournament, after being left out of the 2010 World Cup and playing twice at Euro 2008.
"I'm not focusing on whether Karim scores or not," Blanc said. "He's an important player for us, and showed he had a good understanding with the wide players against Ukraine."
Blanc made Benzema his No. 1 striker as soon as he took charge nearly two years ago, and has stood by him ever since. Benzema repaid that faith with crucial goals in Euro 2012 qualifying, and further strikes in prestigious wins against England and Brazil.
"For me, Benzema is among the best strikers in the world, he's up there with (Zlatan) Ibrahimovic," France midfielder Yann M'Vila said. "I'm not worried about Karim, because when he doesn't score he creates chances for others."
But Blanc is facing calls from some sections of the French media to try playing Benzema alongside Olivier Giroud, the French league's top scorer with 21 goals this season for champion Montpellier.
Giroud is a tall target man who holds the ball up more than Benzema, who tends to drift out wide to find space when tightly marked — like he did in the 1-1 draw against England in their opening Group D match.
"People say Karim peels off too much, but he often does that for Real Madrid," Blanc said.
However, at Real Madrid, Benzema is also there as a provider for top scorer Cristiano Ronaldo, which is less the case with France since he is supposed to be the team's main source of goals.
Blanc has so far ignored the calls to pair Benzema and Giroud together, pointing to how other teams also sacrifice one of their forwards for the sake of the team's balance.
"I'm not the only one," Blanc said. "Germany has the same problem as us. They have (Miroslav) Klose and (Mario) Gomez, but only one of them plays. It's the same for the Netherlands with (Klaas-Jan) Huntelaar and (Robin) van Persie."
Benzema has yet to appear before the media since the tournament started.
Before the opener against England, he said: "I don't know if I'm in the form of my life. I'm only 24, I hope there will be other times. But I do feel really good. I've gained belief in myself, both with Real Madrid and with France."
Now he has to prove it at Euro 2012.