Henry - who became an Arsenal legend and the club's record scorer before leaving to join Barcelona in 2007 - believes the "fairest solution" would be to replay the match following his handball in the build-up to the vital goal, scored by Gunners defender William Gallas.
The French Football Federation, meanwhile, feel they should now concentrate on looking ahead.
However, Wenger - who famously agreed to a replay of an FA Cup tie against Sheffield United in 1999 - believes they have a responsibility to uphold the spirit of the game and make the gesture of a replay.
"I support France and it is embarrassing to qualify the way we qualified. We want to beat Ireland properly and that didn't happen," said the Gunners manager, who has turned down opportunities to manage Les Bleus.
"At the end of the day you can talk and talk and talk, or you replay, or you don't replay. Thierry Henry was the big loser in this story. If he had come out [at the time] and said it was handball, half of France would have said, 'how crazy is he, not to get us to the World Cup?'
"If he doesn't say it straight away, he is also guilty. The problem is not Thierry Henry, it is above Thierry Henry. He played here for 10 years and has always been super fair.
"He has come out and said 'I made a mistake, I touched the ball with my hand'. That is honest. Let's make sure it doesn't happen again because we could see it every week."
Wenger, who was in Paris for the midweek game working as a pundit for French television, added: "Football and sport in general is full of heroes who have cheated 10 times more than Thierry.
"For me people who bought referees, who took drugs, they are the real cheats in sport. Thierry Henry has years of fair behaviour behind him and he today is singled out in the wrong way.
"A player of his stature has a massive pressure on his shoulders and if somebody has to do something for Thierry, it is French football and France as a country, not to leave him out there alone against the whole world.
"France has to say 'yes it was a handball and we offer a replay'."