Arsène Wenger does not, in the normal run of play, give interviews. Or rather, Arsène Wenger does not give interviews beyond the pre-match briefings and the post-match reactions, when he stands in front of all those little logos and explains why his Arsenal team have won, or could or should have won.

They are for the aficionados, these after-match managerial interviews, absent in shade and contemplation, full of the lingering fizz and frustration of these men who send out their teams and then can mostly only watch, sit, stand, fidget, glower, chew nails and gum.

Wenger, though, is always interesting. To begin with, he does not seem quite right as a football manager. Rarely has someone looked so good in a suit and so bad in an anorak. Tall, fastidious, an air of the intellectual; not as rakish as your average structuralist, perhaps, but definitely un homme serieux.

Such niceties didn't trouble English football when the little-known Wenger arrived in 1996 to coach one of the few English clubs to rival Manchester United in fame and éclat. He instantly became "The Professor", and has so stayed, through the two "doubles" and the unbeaten season, to this day retaining the undimmed admiration of a large part of north London and beyond.

But it's a good nickname, and not just because Wenger has a master's degree in Economics from his home-town university in Strasbourg. His approach is a touch more donnish than is usual. (I once asked Kenny Dalglish of Liverpool for his prediction on a Wembley final: "It'll be sunny" was his entire response. He was right, though.)

The Arsenal manager also speaks that French-accented English which lends great authority even to the statements of Chief Inspector Jacques Clouseau. To listen to Wenger's careful elucidations, adorned by mots justes occasionally and winningly misplaced, is to be intellectually convinced, that, yes, they were robbed.

Who better, then, to bring some sagacité and finesse to the current debate about the tawdry rapaciousness of the culture of our football? Even those untouched by the English mania for its national game must be aware of the enthusiastic extramural activities of certain leading players. And if not, someone recently heard a Premier League club grandee offer this helpful summary: "We pay them too much money and they fuck everybody."

But, Arsenal usually explains, if Wenger did agree to expound and dilate on such matters, he would have no time to coach football. And, it has to be said, if you look elsewhere for those most gifted in defending the game off the pitch, they have a point.

Today, though, is different. Wenger is sitting high up in Arsenal's Emirates stadium, in one of the private boxes (from £4,500 a game, in case you're wondering) appointed in the style football likes: four-star hotel. And he is happy to talk about football and morality, its duty and beauty, how good a player he really was, and whether, in fact, he's too intelligent to be a football manager at all.

It's because he wants publicity. Not for himself – nothing so flagrant – but for Arsenal's work in the community, here in north London and around the world: in South Africa, Bosnia and Kenya; in the Chernobyl-devastated town of Chernigov; in Egypt and Israel, fostering better relations between Arabs and Jews. Home and abroad, football as a force for good, the allure of the great name opening doors, eyes and opportunities, bringing coaching, flattering attention and lasting help.

The surprise is, amid all the hype and the hoopla – the trivia and the tosspots, the criticism and the disdain – that football doesn't make much more of this work. Arsenal are the pioneers: today is a celebration of 25 years of their community programmes, 5.5 million hours of them, involving 1 million people, helping the aged, the young, the excluded and the unfortunate. The Premier League clubs will invest about £100m in the community this year. In addition, the Premier League centrally will spend £136m on football-related community projects at home and internationally.

A bit too worthy, this aspect, possibly; not sexy enough – not next to Rory Delap's long throw, a tactic employed by Stoke, who on the day of our meeting were Arsenal's next opponents, a fact which has taken up quite some time at Wenger's press briefings following the community-programme celebration earlier on. This had been addressed by Wenger in true Professorial style: he asserted that the achievement of happiness for a football club could be divided into three parts, numbering results on the pitch after respect for the club's traditions and the responsibility to help the community. "The moral values I've learnt in my life I've learnt through football," he said. "As a club we have an educational purpose, to give back to those people who love Arsenal so that they learn moral values from our game and how we behave."

Not the sort of stuff, on the whole, that you get from the "ashen-faced" Ron Knee, Private Eye's satire on the archetypal English coach. (My own real-life favourite was the remark made by one manager about Neil Webb, sometime England international midfielder, later a postman: "Webby's not just special. He's special special.")

Up in the VIP box, Wenger later expands on football and life, duty and beauty. "I believe a big club must have the ambition to win with style ... You know, there is a famous saying, that the only way to deal with your life is to transform it into art, every minute of your life. Football is an art, like dancing is an art – but only when it's well done does it become an art. If you see me painting, that is not an art. If you see my wife painting, that is art."

Several things there. First, Wenger has more of a sense of humour than you might imagine; he even made a joke earlier on about Rory Delap. Second, he has created at Arsenal teams that insist on such style; even, some say, at the expense of winning, although he is too sensible to confirm it outright. Third, he has a wife and a young daughter who remain sensibly private: his wife, a former international basketball player, watches every Arsenal game, but at their home in the north London suburbs, on the television. "She is not a fanatic but she likes watching sports," he says. "No, she does not have much choice..."

Does he paint? No. He is 60 now, with no plans to retire. Does he have other interests? Yes, but football dominates. "You know the story about the guy who's a promising pianist? One day he goes to a concert and he hears a fantastic pianist. So he goes to see him after the concert, and says to him, 'I would give my life to play like you'" – Wenger pauses for effect and emphasis – "And the pianist replies, 'That's what I have done.'"

It's 7:30 in the morning at Haverstock School, the comprehensive below Hampstead, north London, that is partly responsible for the Miliband brothers. The sports hall is full of 11- to 14-year-olds ready to play football. The early start, they say, "wakes you up". It also encourages them to come to school. Young Abubakar has already had trials with Everton and Reading; Mohamed would love to be a professional footballer as well. "Tell Fabregas to call me," he jokes.

Shortly thereafter, a team-mate of the said Arsenal captain arrives: Bacary Sagna, the French international full-back. He has travelled from his home in the suburbs. He joins the Arsenal community staff in a bit of coaching and chatting to the boys. Sagna is also involved in other community initiatives, including the Arsenal Double Club, set up after the 1998 league and FA Cup triumph to use Arsenal and football as a hook and incentive to learning, in schools, on the local estates, in prisons. It's a frame of two halves: 45 minutes with Arsenal-related learning aids, 45 minutes playing football.

"I'm here to make them believe they can realise their dreams, like I did," says Sagna, "and to tell them to do well at school. I could have failed; they need something to fall back on." Sagna is clear that he is a role model: "It's a massive thing. When you're young you want to be like the footballers, to act like them. If the footballers do something wrong on the pitch or off the pitch, they want to do the same thing ... Recently there have been some stories about footballers ... You have to show an example."

Many people will tell you that foreign footballers are much more sophisticated than the native variety, who have rarely travelled so well. The image of the British footballer is overpaid and under-educated. One of their own, the much troubled and much reformed Joey Barton, now of Newcastle United, recently summed this up for the listeners of the BBC Today programme: "Most footballers are knobs," he said.

Even though he is often criticised for fielding mostly foreign players, Wenger doesn't accept their innate superiority. "English players are as easy to coach. The problem is that the Premier League has the best players in the world, and statistically not all of them can be born in England. But we don't have enough English players: we are working very hard on it."

Being Wenger, he draws a comparison with London as an international financial centre with international employees. Mention of finance reminds one that Wenger, famously and rarely, believes in balancing the books. He once outlined for Glenn Moore, The Independent's football editor, how, when Arsenal decided to build their new £390m stadium, he resolved to concentrate on developing young players rather than buying proven ones, also arguing that it was "the best way to create an identity with the way we play football, to get players integrated into our culture, with our beliefs, our values ... I felt it would be an interesting experiment to see players grow together with these qualities, and with a love for the club ... It was an idealistic vision of the world of football."

He is also renowned for refusing to sanction excessive salaries for his players – and this has led several to move on to other clubs for more. So, in that way of journalists looking for easy précis and a simple theory, I had been erecting a philosophy for Wenger and Arsenal of football as a matter of morality, of doing, in that pervasive Labour phrase, "what is right", on the field, off the field, wherever. Wenger sniffed it, rolled it round a bit, and didn't quite give one of those Gallic sighing shrugs which wearily indicate that life isn't so simple.

Balancing the books was merely logical, he replies – not paying players too much was just part of that. Any other way would have led to what happened to Portsmouth, the Premier League club recently placed into administration. Fabio Capello, the England coach, believes the heady mix of youth and too much money is the root of all off-field problems – so does Wenger agree that footballers are generally over-paid? "That is not for me to decide. That is a society choice. My target is to make the players as rich as possible within the financial constraints of the club. My target is not to give them less money. I'm happy to make them rich."

The subject of the players' behaviour receives similar circumspection. "I believe you can exaggerate the responsibility of footballers, that they should all be candidates for Paradise," Wenger says. "Private life is private life. Off the pitch, there is private life, and the rest is social life, where of course you have to behave responsibly."

In France, though, "John Terry would have made zero headlines," he says. Was this because the French are more sophisticated? "I wouldn't want to say that. I don't say it's better, just different." The press is nosier here, though, and privacy laws are less strict: "In some ways England is more liberal than France, but I also find it more intrusive. But when you go abroad you have to accept the ways of where you live. I have to respect that."

So: Easy Theory 0, Wenger 4. "Are you," I ask him, "too intelligent to be a football manager?" "You can never be intelligent enough," he replies.

it's 3:30 in the afternoon at St Mary Magdalene Academy in Islington, north London. A small boy has just done a double take, similar to the kid in the television advert who spots Lewis Hamilton by the roadside. He has noticed Manuel Almunia, the Arsenal goalkeeper, on the way to a Double Club session, involving small boys and girls throwing a ball at him and shouting out numbers in Spanish. Almunia doesn't drop it once.

Whatever else, foreign players are clearly a considerable advantage for local schoolchildren anxious to acquire a second language. French is particularly well served, and Spanish; German has suffered a little since Almunia's predecessor, Jens Lehmann, departed, but as one of the community workers puts it, "Arsène has stepped in from time to time." (Indeed Wenger speaks French, English, German and some Italian, Spanish and Japanese – he coached in Japan after time in France and Monaco and before Arsenal.)

There is a clause in the players' contracts covering these community activities, but Arsenal have never had to rely on it. Almunia enjoys, he says, "seeing the kids happy". He has also worked with the Teenage Cancer Trust, a former Arsenal "Charity of the Season", the scheme responsible for raising £2m since 2003. "That was really difficult, visiting hospitals and seeing kids with cancer," he says. "It opens your eyes. Footballers live in a bubble – sometimes it's good to get into the real life."

As you can see, goalkeepers tend to be thinkers (other custodians have included Arthur Conan Doyle, Albert Camus, Pope John Paul II and the Nobel Prize-winning physicist Niels Bohr). It's probably all that time spent alone. For the record, Almunia thinks the current bad publicity goes with the territory: you get the money, so you have to take the bad times with the good. He even thinks that journalists are just doing their job, providing what people want to hear: "I'm interested in gossip. People like to have things to talk about in the pub."

Back in the VIP box, Wenger is defending Britain: "I like to live here," he says, "if I didn't I wouldn't have been here for 13 years." The British are more optimistic than the French. "There are plenty of aspects I like in this country. For example, the passion, the generosity. This kind of work that we have been celebrating today, you wouldn't find one club in France, not one, that does that. The work for charity that exists here doesn't exist in France in that quantity. Unfortunately, for every human quality, there is a weakness when it is put to excess."

Wenger is talking about the ugly side of football passion, the racist chants and worse, directed at him in particular from opposition supporters, because of his accentuated foreignness, the Professoriality. "It's the kind of racial abuse that is a hate of difference," he reflects.

Difficult, though, I say, in a sport where the dynamic is rivalry and hyping of difference, even in the same city. "I ask you the question: do you need to hate the other club to love your club?"

Indeed. But his point about passion, weakness and excess is applied by some to him. There is passion and pragmatism as well as calm and logic: he does get a bit carried away at times. In short, he is often called "a bad loser" – "Arsène Whinger". He didn't demur when I put it to him that as a son of Alsace, he has elements of both the French and the German about him (his parents ran a bar and car spare-parts business). If there had been time, I'm confident he wouldn't have been as keen on my view of him as a mixture of French flair and passion and German calm and efficiency. (Stereotype, by the way, is "stereotype" in French and "stereotyp" in German.)

In the game at Stoke to come, Arsenal won, despite, yes, the Rory Delap long throw. But there was also a horrific tackle which broke the leg of Arsenal's young Welsh player, 19-year-old Aaron Ramsey, savagely illustrating the fragility of a football career. Afterwards, in the bright light, Wenger called the tackle unacceptable, and made the point that three broken legs for his players in three years was no coincidence, bringing a furious response from the Stoke manager, Tony Pulis.

Wenger, like other extremely successful football managers such as Alex Ferguson and Brian Clough, does not play the game. "I come out honestly with what I think," he says. Is he a bad loser? "I don't deny I'm a bad loser, because in my job if you're a good loser you don't go a long way. I have been 27 years in this job and I've won more games than I have lost, you know." (And in the early days, he was often physically sick if he lost.)

Some object to the lofty air of the high ground about Wenger, a feeling that book-balancing and home-growing confers an invincible superiority, even when they lose. But that is to ignore the wry amusement, the warmth, the droll and the nuanced in him. I ask him about his professional playing career, for example. Just the 12 appearances for RC Strasbourg. Was he any good? "Better than people think," he says firmly, before adding that nobody can check because there isn't any video.

I have one last question: isn't it odd how similar his first name is to the club's? Yes, he replies. "You could call it coincidence, I prefer to believe in fate." Is he religious? Being Arsène Wenger, he says he is more interested in religions than religion. And now he really has to go.

Back at Haverstock School, Sagna is taking aim at a target bearing the logo of the 25th anniversary celebrations. Watching is Alan Sefton, the head of Arsenal in the Community, celebrating 24 years himself, and, not surprisingly, full of it, from the early days of sponsoring the local bowls team to its current sports traineeships and the Arsenal Learning Centre, part of the stadium project which has created nearly 2,000 long-term jobs and 2,500 affordable homes. It's moving to watch people who have been given help talk at the celebrations. And not bad marketing, either, I suggest. "There are," says Sefton, "easier ways of selling tickets."

The football continues. Abubakar releases a kick of intimidating power and energy, misses, and smiles; a smaller, frailer boy scores two goals and then takes a discreet break for a puff on his asthma inhaler before dashing back: I can see what Arsène and Arsenal meant and means. Sagna hit the target, by the way.