The Cÿte d'Azur is the favourite European playground of the rich and famous. Yet it doesn't have to cost a fortune to sail along its shores. Simon Redfern books a berth on easyCruiseOne

Charles Deville Wells, the original (but not the last) man who broke the bank at Monte Carlo, won more than a million gold francs during his three-day spree in 1891. I had always fancied visiting the Côte d'Azur myself, but felt I would need luck of about that order to be able to fund the trip, a view confirmed by a day-dreaming look at some of the hotel rates on offer for this time of year.

A single room in Monte-Carlo's Hermitage? They might be able to squeeze you in for £295 a night (breakfast another £17). The Byblos, St Tropez? Not much on offer under £300 a night there either, and you'll be lucky to get that unless you've booked many months in advance. How about the Negresco, in Cannes? Well, a little suite will set you back £560 a night.

And then there was Stelios Haji-Ioannou and easyCruiseOne. Which is how I came to be moored off St Tropez one balmy evening last week, leaning casually on a ship's rail, a cocktail in my hand, within hailing distance of Gwynneth Paltrow a few yachts down and cocooned in the knowledge that my bed for the night cost just over 30 quid.

In the early 1900s, St Tropez attracted artists, including leading exponents of Fauvism, a movement characterised by bright colours and innovatory use of form. So they would probably have approved of easyCruiseOne, which is bright orange, inside and out. And, like the Fauves, Stelios is experimenting with form; he has taken the traditional cruise format and turned it on its head, much as he did to budget flying with easyJet.

Traditional cruises are often sold as an all-in package, which includes meals and on-board entertainment, with the ports of call almost as sideshows. Stelios, in contrast, while not actively throwing you off the ship when it docks, seems keen for you to enjoy as much time ashore as you can. EasyCruiseOne potters up and down the French and Italian rivieras, putting in at a different port each day in a weekly cycle: Friday is Nice, followed by Cannes, St Tropez, Monaco, Genoa, Portofino and Imperia before returning to Nice. In most ports, you dock around 1pm, and the requirement is only that you be back on board by 4am, before easyCruiseOne sets sail for the next stop. Other innovations include flexible booking arrangements; you can get on at any port you like, and stay for as little as two nights.

In one respect, though, Stelios might have made a miscalculation. "I'm trying to get younger people to cruise," he says (the average age of the Brits who took a sea cruise last year, more than a million of them, was 54). And that, combined with the dawn curfew and rock-bottom rates, led to suggestions that he might need to rename the operation Chav Cruises. But, apart from a rumour that two sparky young North American lasses had made a Geordie lad an offer that included more than a goodnight kiss, and a certain amount of energetic dance-floor action in the bar in the small hours that led to the odd self-inflicted flesh wound, I saw nothing much to frighten the horses during my week on board.

What I did see were a bunch of people of all ages who had, like me, worked out that the true secret of easyCruiseOne is that it is not a cruise at all; it's a floating hotel that offers a way of seeing the historic, and often beautiful, Côte d'Azur at a fraction of the normal cost.

On that basis, does it work? Everybody I talked to among the 70-odd passengers on board when I joined (the total capacity is 170) seemed to think so. Lorraine, a Dubliner who as a ship's purser herself should know what she's talking about, said: "I was a bit wary at first, coming on my own, but everybody's been friendly, asking me if I'd like to join them sightseeing ashore, or go for a meal in the evening. I once took a job on a Caribbean cruise liner and left after five weeks, the conditions and the food were so grim. This is far better, at a fraction of the cost."

Lizzie, a young American studying in Rome, who had flown to Nice and was catching the train back from Genoa, agreed. "I had a few days spare, and thought, 'Why not?' I'll be going back to the States in the summer, and may never get the chance to see all these places again, so I think it's fantastic."

That is not to say that there weren't hiccups; even on a ship this small - around 4,000 tons, with the main action concentrated on only three decks - having the lift out of order was more than an inconvenience for some. Also frustrating was that, although a variety of excursions were advertised at each stopover, many were cancelled when too few passengers signed up. And some of Stelios's local agents need a bit of a talking-to; charging £71 for a 20-minute helicopter ride over Monte Carlo seems a bit rich when the same trip is advertised locally for €45 (just over £30).

But, given that the inaugural cruise was only on 6 May, the fact that the operation is still bedding down is excusable. And on the subject of bedding down, the cabins aren't bad at all; comfortable twin mattresses on the floor which can be pushed together to make a double, a stylish sink-and-shower unit, and adequate if not exactly capacious storage space. My only criticism is a total absence of portholes in most of the cabins, due to a change in floor levels when this former gambling ship from Singapore was refitted. As I'd forgotten to pack an alarm clock, waking up in pitch-dark meant that my hours of rising were, shall we say, variable. So I was grateful for the all-day breakfast on offer, although by the time I was eating it on some days I could have also chosen from a lunch menu of pizza, salad, burgers, and the like; good pub-grub fare, and priced accordingly.

It's traditional when writing travel articles to mention the places you have visited,so I should tell you that Nice is lively, with a lot of the buzzier bar/boutique/clubbing action centred around the Vieux Nice area just east of the port. The beach around the grand sweep of the Bay of Angels looks enticing, though I was too mean to put up with the mercenary French habit of charging you to lie on the sand. There are a few strips of municipal beach, but they get very crowded.

The same applies at Cannes, an altogether more staid place, though it is trying to move with the times. These days, you are more likely to be mowed down by one of the swarms of inline skaters as you promenade on La Croisette than suffer the fate of the flamboyant dancer Isadora Duncan in 1927, strangled by her own scarf when it caught in the wheel-spokes of her Bugatti.

St Tropez was a pleasant surprise; prettier and less expensive than expected. If you're a barfly like me, have a scoop at Le Café on the Place des Lices, which claims to be the third-oldest bar in France, founded in 1789, a year in which a few other things were going on in France.

Imperia was the surprise of the Italian leg; a friendly laid-back little town with good beaches and portside cafés. EasyCruiseOne seem a little ashamed of it, calling it "Imperia for San Remo", but those of my fellow passengers who bothered to take the bus for the 45-minute journey to the better-known resort all returned saying they preferred Imperia.

Monte Carlo, though, was a disappointment. Apart from the Musée Océanographique de Monaco, dedicated to deep-sea exploration with a splendid aquarium to boot, it was a bit, well, dull. To pass the time, I was forced to visit the casino in the evening - take your passport or driving licence with a photo as ID; whatever anyone tells you, they won't accept copies - and have my first bet at roulette (I've led a sheltered life).

Now, I can't promise this will happen to you, but I can only tell it how it was. I sat down, chose a number at random, black 8, and plonked €5 on it. The wheel span and the ball whizzed round before dropping into a number. Black 8. Charles Deville Wells would have been proud of me.