Wenger confirmed Giroud is expected to be out until at least December with an ankle injury but the Arsenal manager stressed he was in no rush to buy another forward.
Arsenal scored twice in the final seven minutes to grab a 2-2 draw at Everton in the Premier League and avoid another demoralising defeat on Merseyside.
The 1998 champions lacked conviction going forward after missing two early opportunities and eventually lost to Germany 1-0 on Friday.
France's opening match at the World Cup against a Honduras side with a reputation for aggression promises to be a bruising encounter on Sunday.
Olivier Giroud and center half Laurent Koscielny have been cleared to take part in Thursday's training session after sitting out the previous day's practice.
Franck Ribery's injury means coach Didier Deschamps is finding a way to accommodate them both by shifting Benzema onto the left flank.
France had the majority of possession but Arsenal forward Olivier Giroud missed several chances and failed to add to his international tally.
Giroud scored twice and winger Mathieu Valbuena set up three goals as France began their World Cup preparation with a 4-0 exhibition win over Norway.
Olivier Giroud scored in the first half to give Arsenal a 1-0 win over West Bromwich Albion and leaving the Baggies uncertain of their status in the top flight.
Arsenal took a big step to securing their place in the Champions League for a 17th consecutive season after a comfortable 3-0 home win against Newcastle United on Monday.
Wenger took a risk by picking Arsenal's old guard against West Ham but it paid off with a 3-1 win as his weary side regained fourth place in the EPL.
After extra time ended 1-1, Arsenal's players scored all of their penalties - the last by Santi Cazorla to beat Wigan 4-2 on penalties.
Giroud scored two of Arsenal's three goals in the final 22 minutes as his team became the first to advance to the last four of the cup.
Arsenal cruised past Sunderland to keep pace in the Premier League title race, with goals from Olivier Giroud, Tomas Rosicky and Laurent Koscielny.
Arsenal were held to a 2-2 draw at Southampton, leaving the door open for one of their rivals to seize the Premier League lead.
Arsenal survived a late scare to regain top spot in the Premier League with a 2-1 victory at Aston Villa on Monday.
Giroud has not played for title chasing Arsenal since scoring in their 1-0 win at Newcastle United on December 29.
Nicklas Bendtner, Olivier Giroud are not fit for Arsenal's upcoming game against their city rivals.
Arsenal go into the match with a one-point lead over Manchester City and Wenger said he was proud of the fact his side accumulated more points in 2013 than any other side in the league.
Olivier Giroud ensured that Arsenal will finish the year at the top of the Premier League standings by scoring the winner for the Gunners in a 1-0 win at Newcastle.
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