This summer, some 100,000 young people from around the world – mostly between the age of 15 and 30 – will gather outside a village in the middle of France. They've been arriving here since June, to pitch tents, strike up friendships, enjoy plenty of music, and they'll continue to come until September. But this isn't some Gallic Glastonbury – it's a Christian community, and the crowds will sing psalms, not pop songs.

At the heart of Communauté de Taizé, named after the small village near the site, are over 100 monks, who live together very simply, in a life devoted to prayer, singing and silence. Drawn from over 30 different countries, the community is ecumenical, with Catholics and Protestants worshipping together.

And, even more unexpectedly, since the end of the Fifties, Taizé has been attracting young people in ever larger numbers, and from ever more far-flung destinations. Teenagers and young adults make the pilgrimage, usually for a week, joining the brothers in prayer three times a day, attending bible groups and helping out with chores. During the summer months, there will be a population of 3,000 to 4,000 at any one time, drawn from about 70 different countries, camping or staying in basic barracks, very cheaply (it's just eight euros a night for bed and board).

At a time when church attendance is falling in western Europe and religious leaders fret about their ability to attract young people, why are believers flocking in such vast numbers to a monastery in rural Burgundy? What is it that Taizé offers the teen spirit?

"So many young people were leaving the church – and here, people were coming," says Brother David, aged 38, who moved to Taizé from Portugal when he was 20. "It's important we support their search and give them a place where they really can go. It's not to tell them what they should or should not do, it's to let them have that time of meeting with themselves, with others, and with Christ."

Whether or not you believe in setting aside time to "meet with Christ", Taizé is obviously offering something attractive to an age group that most parts of the establishment have trouble communicating with. I'm not a Christian, although having been raised a Quaker, I'm comfortable with the idea that communal silence can be a powerful and beneficial thing. I'm in its target age group. But, like many 25-year-olds, going to church isn't something I do – and certainly isn't the way I'd choose to spend my summer holidays. What's the attraction of Taizé for people of my generation?

For a start, the church itself is unconventional. A long, low building – with shutters and panels so that it can be opened up to fit the size of the congregation – it has no architectural features to speak of. There is nothing in the way of religious iconography. Neither altar nor crucifixes stand inside. The walls are speckled brown, the carpet is orange, and there are twinkling candles and softly glowing orange bulbs in what look like casually-strewn wooden boxes at one end.

There are no pews – the youthful congregation sits cross-legged on the floor, slipping off our shoes. The brothers, in their long white robes, sit in a middle section, but there's little separation. The building feels more like a Japanese dojo than a church. But it also looks cosy and welcoming, and, to me, pleasingly casual and egalitarian. Brother David later tells me, "no one is better than anyone else in prayer".

Taizé prayers are pretty different to those at a conventional Sunday service, too. Instead of traditional hymns, there are simple, repetitive chants, sung in many languages. Often only one or two lines long, but with hauntingly beautiful tunes, the idea is they're easy to pick up, with the repetition creating a meditative effect.

I'm no singer – even my closest friends have never yet persuaded me to join in with karaoke – yet I found the resonance and repetition of the songs sung here to be astonishingly peaceful (although singing 'Hallelujah' and 'Bless the Lord' does feel odd when you don't actually believe in Him).

There's no sermon or preaching, although a brother reads a short passage from the Bible. And in the middle of the service there is period of silence for 10 to 15 minutes. It's this silence that's mentioned again and again as one of the most appealing parts of the Taizé experience, according to regulars. We live in a noisy world – and for teenagers who have grown up with mobiles, Facebook and Twitter, a permanent iPod plugged in, to sit in silent stillness can be a revelation. As 28-year-old Johan Vaneeken, from Holland, tells me: "There are not many places or times in our Western civilisation to be quiet, to be yourself and contemplative – that's very hard to do at home. So I think it's very important there's a place like this."

Yet for a place that is so peaceful, the Taizé community has a turbulent past. The monastery was founded in 1940 by Brother Roger, a young Protestant who grew up in Switzerland. He wanted to gather a small group of men to live as a "parable of community" – to try to live like Christ, together.

Rather than keeping his head down in Switzerland during the Second World War, Brother Roger got on his bike and cycled to France in search of a place to establish a religious community. Not far from Cluny – the site of a famous Benedictine monastery – the monk found an old farmhouse in Taizé, where a woman implored him to stay. "For Brother Roger," one of the monks tells me, "this was a sign, God speaking through an old woman, a poor woman, and so he bought the house." And lo, the Taizé community was born!

It soon became known as a haven for Jews, Christians and anyone else fleeing for their lives. Its founder was forced to return to Switzerland after the Gestapo arrived one night to arrest him, but he returned after the war and in 1949 the first community of seven brothers was established. Young people started to show interest in the early Sixties, with the arrival of structured youth meetings.

To begin with, young visitors stayed in another village about four kilometres away, because as Brother Paolo says, "nobody really thought monastic communities and young people could mix". But the meetings quickly moved to Taizé itself. Brother Paolo, aged 55, who left England for Taizé one summer at the age of 20 and never left, explains: "They found, not only was it possible [for them to mix], but there was a strange kind of correlation between a searching – which for so many young people is very intensive, trying to think what they're going to do with their lives, what hopes they have, the struggles they have – with that of a monastic vocation, where you are continually trying to rediscover the meaning of your life." By the turn of the century, Taizé was attracting several thousand people every weekend of the summer.

But if you open your doors to everyone, you are likely to attract a share of troubled souls. On 16 August 2005, Taizé was shaken when a mentally ill young woman stabbed the 90-year-old Brother Roger to death – inside the church, right in the middle of the service.

"It's a mystery. We cannot understand how something like that could happen," says Brother David now. "In the beginning of the prayer a woman comes close [to Brother Roger], and everyone thought it is probably the mother of one of the children sitting by him. She had a knife and she killed Brother Roger. The first ones to see were the children; they saw the blood."

The other brothers carried him out, but he died before a doctor could reach him. Astonishingly, the prayers continued – in the large room, people heard a cry but didn't realise what had happened till the end of the service.

Brother David is clearly bewildered when recollecting the tragedy, six years on, but defiant. "Even in that difficult moment, even in the shock, it brought the brothers closer to one another," he insists. "It was also very beautiful that there were 3,000 people here, sharing the prayer with us. You could say, it must have been horrible, but the people who were here were saying at the end of the week that they had found peace. This peace is much stronger than what we lived in that one moment."

While the services are certainly very peaceful, 4,000 young people in one place is never dull. At meal times, in small group sessions, and round the social area at night, there's a constant hum of chatter, summer romances sparking and in-jokes being vigorously repeated. But you can also hear people having the sort of earnest discussion of their spiritual experiences that would be sneered at in most British schools.

Taizé is keen to attract British teens. Speaking of his own first experience of visiting, Brother Paolo says: "As a 16-year-old boy, I was moved to tears a couple of times during the week, by the silence in the church in particular, just because it was beautiful. I was also so happy to meet people my age who were keen to talk about things that mattered. At school, it's not easy to talk about things that matter – you're frightened of being made fun of."

I meet two school groups from the UK, and another five arrive the day I leave. Some are from faith schools; others are inner-city comp kids. A number are obviously religious, while some are self-proclaimed atheists who just came out of interest.

Chelsea Allgeier, aged 16, from Hove, takes time out from chatting with boys to inform me that, "I'm a Catholic, and I'm from a religious family, but I don't make it every Sunday. Being here has made me believe more. The whole world should be like this, it's lovely."

She's at camp with Sam King, aged 15, from Gloucester, whose RE teacher has bravely herded a group of non-religious boys to Taizé for a week. "I would have said I was an atheist, but it's changed me to be open-minded, I think," says King. "The silence lets you reflect on yourself, and the prayer and singing show it's a community. I respect this place – it brings people together." He plans to come back next year.

For lots of the kids, Taizé becomes an annual pilgrimage. Katya Lozar, aged 25, from Slovenia and my roommate, is here for the seventh time. "I keep coming back for the spirit of Taizé, the people and the silence and the peace. I go to a Roman Catholic church, but here it is more free."