Thus, Wilshere swells the ranks of footballers caught on camera smoking yet denying it is a regular occurrence. Indeed, his Arsenal team-mate Mesut Özil was pictured smoking a cigarette on a yacht in Ibiza in 2011, while he was still at Real Madrid. Özil's excuse? "It was because I lost a bet, and therefore only a one-time thing. I assure you: I do not smoke."
Characteristically, Wenger claimed not to have seen the Wilshere story. But when informed of the player's misdeed, he said: "I disagree completely with that behaviour. I need to have a chat with him about that.
"There are two things. When you are a football player you are an example, and you don't do what damages your health. You can smoke and drink at home and nobody sees it, but when you go out socially, you also damage your reputation as an example."
A spokesman for Wilshere claimed that he was only holding the cigarette after losing a dare, saying: "Jack was with team-mates and friends. One dared Jack, who does not smoke, to momentarily hold the cigarette as part of a prank. Jack absolutely didn't smoke the cigarette and nor does he condone smoking. Jack is utterly committed to fitness and a healthy lifestyle. In no way is this picture an accurate reflection of his attitude to smoking."
Such a denial was perhaps to be expected. These days, footballers are insured for millions of pounds, and a signed non-smoking declaration is a common feature of medical insurance policies.
Though he grew up in an era and in an area where footballers smoked freely and often, Wenger appreciated that times had changed. "Yes, of course things are different," he said. "I experienced it as a footballer on coaches after a game, when you didn't see each other, there was so much smoke on the coach.
"But times have changed and English society is very sensitive to smoking, much more than France, than southern countries, so it's a bit more shocking here than somewhere else."
Wenger's attitude is unsurprising when one considers his history of dealing with players' vices. He grew up above a bar in Alsace and saw at first hand the damage that alcohol could wreak. He was one of the first Premier League managers to ban alcohol in the players' bar after games and during his early days at the club also banned players from drinking on the team bus. He said at the time: "To play at the top level you have to have control over your life, and part of that is to do with mental strength."
The Football Association had no comment to make and, given that there is no evidence of Wilshere smoking while on international duty, it is content to allow Arsenal to deal with the matter internally. Tobacco is not explicitly mentioned in the England players' code of conduct launched last year, and there is no suggestion that Wilshere's place in the squad is under threat.
England manager Roy Hodgson used to be an avid cigar smoker until his wife stopped him.
Indeed, Wenger was keen to underline Wilshere's value to the squad, claiming that he was close to rediscovering the lightning burst of speed that has made him such a dangerous opponent in the past.
Could he still do a good job in the centre of midfield for England? "Yes," Wenger smiled. "Even with one cigarette he will be good."