Andrew Brown appreciates the quiet and the genteel atmosphere on Marie-Galante

I did not realise quite what an extraordinary place we had found until I was waiting one afternoon in the minibus that goes round the island from outside the chemist's shop of Madame Adeline Miraculeux-Bourgeois.

I did not realise quite what an extraordinary place we had found until I was waiting one afternoon in the minibus that goes round the island from outside the chemist's shop of Madame Adeline Miraculeux-Bourgeois.

The minibus out of Grand-Bourg kept Caribbean time and was equipped with the standard third-world safety devices: a prayer taped to the roof above the driver and a relic dangling from the mirror. I waited beneath a blasting sound system while other passengers climbed on for half an hour, watching two chickens feeling even more subdued in a basket on the floor.

But something happened before we set off that I can't imagine seeing on any other island. The woman across the aisle finished the sandwich she was eating from a paper bag and rose carefully. She left the minibus, and picked her way across the weed-strewn lot until she came to a plastic wheelie bin, into which she dumped the wrapper of her sandwich before progressing in a stately fashion back to the bus and the chickens. A developing country where people use litter bins, to me, is something close to paradise.

The island of Marie-Galante, off the Atlantic coast of Guadeloupe, was one of the first parts of the West Indies that Columbus saw and he named it after one of his three ships. Not a lot has happened in the past 400 years. Ever since the Indians were expelled to neighbouring Dominica and sugar-cane plantations started, the slaves and their descendants have farmed the island. The French have administered it. Excitement has stayed away.

The island is miraculously bourgeois, genteel and French. There are hardly any tourists, and fewer than half-a-dozen hotels, of which the biggest has only 15 rooms. There are no beggars and little crime. When my wife was sketching on her own, all the passes made at her were most polite. Everyone speaks French, which keeps the Americans away, while the metropolitan French stay on the larger and far more heavily touristed main island of Guadeloupe, a lurching and sickening 50-minute catamaran ride away. The beaches are spacious, empty, and enclosed by coral reefs.

We had gone there partly to teach my daughter to swim in a place more encouraging than the local municipal pool. For this, the island is perfect. To the east and south-east, the beaches are shallow and protected by a reef very close to the shore: at one, an adult could almost walk the whole way to the reef. It was delicious to drift face down with a snorkel above these shallow worlds: the very white sand giving way to green underwater grasses with purple bladders like tiny aubergine blimps floating above them. Some of the fish were as bright as tropical show-offs are meant to be, but others were so perfectly coral-sand coloured that they seemed just like a few disarticulated bones hovering above the bottom.

There are two dive shops on the island that will take visitors out, but nothing like the full-blown diving industry of Guadeloupe, where every seaside village seems to have at least four diving schools.

On the western side of the island the beaches are less protected and more spectacular. Here is where children learn real swimming, with waves that can tumble them over onto hard rocks and bad-tempered surf that can pull them back off the beach afterwards.

Getting into the sea is no trouble, but getting out of it needs timing and care: the first time we did this, my daughter staggered up the beach, threw herself on the sand like Robinson Crusoe and shouted at the top of her voice. "I've been killed! I've been killed!". Half an hour later she had been coaxed back into the water but was shouting just as loudly that she did not want to come out and could swim for ever. Two days after that, she was deliberately jumping in the biggest waves she could find and shouting "I'm invincible!" Five waves later, she was soggily vincible, knocked head over heels and rolled round and round. But this time she was able to pick herself up and crawl out alone before resuming the game with the surf.

Like any real paradise, it would get excruciatingly boring for the adults. There is little to do on the island except drive around and swim. In the port of Grand Bourg, there are cafés down by the harbour where every bad white haircut of the past 20 years can be seen circling in an eddy of slow time.

You can catch a whiff of Somerset Maugham here, of boredom that thickens the air like heat. But most of the island is full of dignity, energy and a sense that people are getting on with their work. In the interior of the island, the only organised tourism is based around the rum distilleries. Coachloads rattle to the Bielle distillery, down roads built more for the ox-carts that still deliver some of the cane than buses. But even here, the hustling is low key: a few stalls selling biscuits and coconut toffee.

The white rum of the islands is savage stuff: cheap and throat-ripping. A litre of 60 per cent (or about 140 proof) rum costs less than £4. Mixed with half the quantity of cane syrup and a generous squeeze of lime juice it makes a "ti punch". But they also make older, smoother brown rums, which are full of subtle flavours.

The roads are metalled and well-maintained; the traffic is far less hectic than on Guadeloupe - at one stage we were held up by a race of 50 or more cyclists, all wearing helmets in the steaming heat. Later, our journey was broken by what seemed like a cloud of hunched red leaves being blown slowly across the road, which made a crunchy popping sound when I drove through them. I turned back for a closer look. It turned out to be a torrent of migrating land crabs, with red shells and glistening bulbous black eyes, hurrying across the road as if it were no-man's-land, high-stepping past the flattened yellowy carcasses splattered across their path. The next day every trace of the massacre had been scavenged away.

Between the beaches, most of the coastline is eroded to a brutally sharp-edged lacework of foamy brown limestone on which the spray breaks endlessly. At two places the central plateau rises straight from the ocean in spectacular cliffs but the inner plateau of the island is extraordinarily gentle, rising in marshy low-lying land rather than hills through the endless plantations of sugar cane. It is not forgiving stuff. All the farmers wear wellington boots to protect their feet and carry machetes everywhere, even when riding mopeds.

But there are no snakes on the island: they have all been exterminated by the mongooses. In the mornings I would sometimes see a rat running along the branches of the coconut grove outside our hotel window, but even they seemed orderly and bourgeois, scurrying about their lawful business before the sun made life impossible.