Simon Calder: The man who tries not to pay anything

Social networking? Not working, at least for me. Last week, as the pound continued its freefall against the euro, I went online to to try to find a sofa to sleep on in Paris. The idea behind this and similar sites is that you tell prospective hosts about yourself and your travels, so that they can judge whether you look like a safe and rewarding bet as a house guest.

The more I revealed about myself, the more deafening the silence from the people who I hoped might lend me somewhere to snooze after dark in the city of light. Nul points from couch proprietors – which is why I find myself in dorm 214 of the Woodstock Hostel in the ninth arrondissement, location for what I believe to be the cheapest accommodation in town.

When I called to book a room, the "hold music" was "Riders on the Storm" by The Doors – a hit in the same year as the Woodstock Festival, 1969. At the time, the vocalist, Jim Morrison, was alive and well, rather than down and out in Paris, and sick sterling was being propped up with the help of stringent currency controls.

Once again, the pound looks as puny as a Parisian poodle. To stretch your sterling, you can't fault a bed at the Woodstock for €22 (£18).

Unlike many Parisian hotels, this clean and cheerful hostel throws in breakfast and Wi-Fi – but also unlike many Parisian hotels, sheets are not included: €1.25 each, or more than £1 at the current lamentable rate of exchange. Company is included, though. Pity poor Vidya, the New Zealander who, as a casualty of the arbitrary social networking that hostelling entails, finds herself sharing a dorm with the loser who couldn't find a Parisian friend online.

My miserly mission was to spend a couple of days in the French capital on as little cash as possible.

On Tuesday morning the full horreur of the plummeting pound became clear when I asked the man running the bureau de change at the Louvre how many euros he would give me in exchange for £100.

The answer was so shocking that I had to ask him to repeat it: €102.50. In other words, the pound that only last summer was worth close to €150 is now almost at parity. Do you recall the French franc, which used conveniently to trade at around 10 to the pound? Well, the corresponding rate would be Fr6.72 = £1.

By shopping around you should be able to find a much better rate, possibly as much as €1.20 for your pound. But once local inflation is taken into account, prices in the eurozone have increased by one-fifth in a year. That is why we have endeavoured to make this edition of The Independent Traveller a euro-free zone.

Come Albanian leks, UAE dirhams and Uruguayan pesos: you have nothing to lose but your ignominy.

The trouble with these destinations is distance. The pound's best performance over the year has been against the South African rand (see page 8). But Paris will always be more accessible than Pretoria. So to continue my economy drive, I have walked from the Woodstock to the Left Bank to join the 1pm "Free Paris Tour". However, it is now 1.20pm, and a half-dozen of us are waiting expectantly.

The guide, Adrian, says he has some bad news: today's "authentic introduction to continental Europe's most visited city" has been cancelled. Why? Because it is not financially viable. Hang on: surely a "Free Paris Tour" is, by its gratuitous nature, never financially viable. Adrian explains that he works for tips (about €10-€15 per person, he claims), and it is not worth three hours of his time guiding as few as six people.

Instead, I visit three of the city's great museums: the Louvre, the Musée d'Orsay and the new Musée du quai Branly. "Visit" in this context does not actually mean going in, but that is not without its benefits: your appreciation of the structures and surroundings is heightened.

You get a sharper image of the angular perfection of IM Pei's glass pyramid at the Louvre if you are not rushing to see the Mona Lisa. Inspecting the exterior of the Musée d'Orsay is a revelation, from the bronze rhinoceros standing guard to the engraved roll-call of gares from Quimper to Toulouse that this mighty terminus once served. And amid the slinky curves of the foyer of the Branly you can see a good cross-section of the exhibits, from African lutes to a large limestone sphere from Costa Rica.

This gigantic globe is asserted to have spiritual significance, but to me it just radiates stony silence – exactly the response to my doomed couchsurfing quest.

On your bicyclette

Free bikes is the promise of Velib, the innovative municipal bicycle scheme in Paris.

First, search for one of the "stables" of 20 bikes that have been established at various hard-to-find points around the city. Having located one, your problems are only beginning. A computer terminal holds the electronic keys to all the bikes. It took me 15 minutes to discover the right combination of keys to coax it into accepting my credit card (a €1 fee for a day's use, with a €150 deposit) and releasing a bicycle.

The bikes themselves are fine; just what you need for drifting around a relatively compact city. But it turned out to be an extremely tense means of transport.

The erratic driving practices of the Parisians were only partly to blame; more stressful was wondering where and how to return the thing before my train left. As the minutes ticked away towards departure time, I realised that these "stables" can often be full. Eventually, I found one with a space, but vowed next time to travel free by Metro instead. You buy a carnet of 10 tickets from a Metro station for €11.10. At busy locations, travellers will pay the single-journey price of €1.50 to avoid queuing. When you have sold eight, you are in profit and still have two tickets left. Regrettably, in the country that gave the world the word "enterprise", it seems this practice is illegal.