France needed a second-half equaliser by Griezmann to draw 1-1 with Hungary in Budapest on Saturday, a result that nevertheless left them on top of Group F at the European Championship with four points.
The world champions beat Germany 1-0 in their opening game in Munich and now require just a point against Portugal on Wednesday to guarantee a place in the last 16.
However, the lack of goals from their superstar attack of Benzema, Griezmann and Kylian Mbappe has become the talking point — against Germany it was a Mats Hummels own goal that decided the game.
“He wants to score just like Kylian and I, and as a player you need it to feel relaxed and liberated,” Griezmann said.
“He has been really important in our link-up play and I am sure when he gets one goal the tap will open and it will keep running.
“He knows he has the support of the staff and the players and we hope he gets a goal soon, but the most annoying thing would be if he were not even getting the chances.”
Benzema was recalled by France coach Didier Deschamps for the European Championship after a five-and-a-half-year international exile.
It was a controversial decision as Benzema is awaiting trial over his alleged involvement in a blackmail plot involving a sextape and former France teammate Mathieu Valbuena.
Without Benzema France reached the final of Euro 2016 and then won the 2018 World Cup, but there can be no doubting his on-pitch credentials.
The 33-year-old scored 23 goals for Madrid in the season just finished.
Nevertheless, his performance on Saturday earned him a rating of just 3 out of 10 in leading sports daily L’Equipe.
The newspaper pointed out that Benzema “has never scored at a Euro after eight matches and 33 shots”.
Leading writer Vincent Duluc said that “even at 33, even after 12 seasons at Real, the pressure still seems to be getting to him, as is the expectation that he has created but that he is now feeling himself.
“His return remains a great story, but thus far it has been imperfect.”
However there is no question of Deschamps reconsidering his attacking options, for now anyway.
Noel Le Graet, the head of the French Football Federation, told AFP that Benzema’s performance, and that of his teammates, should be seen in the context of the stifling conditions in the Hungarian capital.
“So far he has only played two official games, after two friendly matches, so he is still finding his feet,” Le Graet told AFP.
“He played well in the first game. On Saturday it was the same for all the attackers: the amount of running they had to do without the ball, in 33-degree heat, made it difficult.”