Henri Desgrange, founder of the Tour de France, defined his ideal race as one that finished with a single cyclist surviving. When a friend and I embarked on a series of long bike rides through France with a book in mind, we did so in a spirit we imagined to be as far removed as possible from that ideal. A perfect stage of our anti-Tour would involve a picnic and a snooze on the river bank, some wine tasting or other non-intensive sightseeing interludes; and a comfortable bed in a small hotel after a good supper. Our rides were long, but we hoped they would not be too gruelling. We would avoid steep hills wherever possible, and where not possible we wouldn't be too proud to dismount and walk.
So we pedalled happily down the Loire last July paying no attention to the evolving drama of the world's toughest sporting event, until a text message from Brittany Ferries alerted us to the fact that the Tour would be crossing Normandy on the day of our return sailing from Caen, with a rolling programme of road closures that we should beware. After deciding not to attempt the Pont St Nazaire on our bicycles in a crosswind, we caught a train back to our car and drove north to intercept the Tour near Falaise.
Joining a few spectators beside the road, we watched police motorbikes go past, lights flashing self-importantly, until eventually the word went round: "La caravane arrivée!" It was a carnival procession of sponsor vehicles and floats, with music and dancing girls hurling sweets and junk mail at us. How long before the cyclists arrive? "The caravan lasts for more than an hour," someone said, so we fled the hailstorm of Haribos and missed our chance to fail to spot Cavendish and Wiggins.
The chance would come up again two weeks later, when the start of our ride from Paris to Avignon coincided with the final stage of the Tour, whose brave survivors ride laps of the Champs-Elysées before the podium moment beneath the Arc de Triomphe. We had chosen a Sunday for an easier journey from St Pancras by train and out of Paris on the suburban RER (no bicycles allowed on weekdays during rush hour), and because on Sundays the expressways along the banks of the Seine are reserved for non-motorised traffic.
We could have caught the RER from the Gare du Nord but the chance to ride through central Paris was too good to miss. Turning left at Opéra, we passed the armour-plated shop windows of the Rue de la Paix and rattled over the cobbles of the Place Vendôme to find the Rue de Rivoli guarded by banks of spectators. Turning left again, we rode past the bottiers of the Rue St-Honoré as far as the Comédie-Française where we were finally allowed to turn right, through an opening in the Louvre palace and between I M Pei's glass pyramid and Napoleon's dainty little Arc de Triomphe du Carrousel in the Tuileries gardens. Another opening in the Louvre brought us to the Seine, where we looked down on the riverside expressway: a heaving throng of slow-moving humanity, quite hopeless as a cycle track.
So we stayed on the Quai François Mitterrand (as no one calls the Quai du Louvre) and followed it along the river. We reached the Gare de Lyon, carried our bikes down to the underworld and caught our RER train (line D, for Melun via St-Fargeau) out through the suburbs to a point beside the Seine where we could set off for Fontainebleau, Burgundy and the south. Once again, the Tour had eluded us. Too bad. Ours was a much more civilised cycling homage to the delights of rural France.
This happy state of mind prevailed until I came across a remote country chapel in the Armagnac region of south-western France. Notre-Dame des Cyclistes is a popular halt for cycling pilgrims on their way to Compostela: 1,000km to go, in 12 easy stages of 85km a day, according to the present chaplain who has made the journey six times.
The chapel was discovered, overgrown, by a cycling churchman in 1958 and the following year Pope John authorised its re-dedication to la petite reine. It marked the start of a Tour de France stage in July 1989. Many Tour heroes attended and laid down their jerseys and trophies, as did the race leader Greg LeMond who went on to win the Tour by eight seconds and spoke of his win as a miracle.
The Tour riders may not pause to taste wine, swim in rivers or light candles in Romanesque churches, but their journey is also a celebration and a pilgrimage, and arguably a more complete homage than our self-indulgent meanderings. "To love cycling inevitably means to love geography and, additionally, the different regions," writes Christian Prudhomme, director of the Tour in his website editorial.
According to Mr Prudhomme, this year's tour is dedicated to "medium mountains" such as the Jura, the Vosges and the Massif Central. Their passes may not be as high as those in the Alps and Pyrenees, but the climbs are as steep and can stretch the peloton. On 7 July the Tour will be in the Vosges, tackling the ascent to La Planche des Belles Filles, the only ski resort in the department of Haute-Saône. I had never heard of it until I read Mr Prudhomme's description. Apparently the place takes its name from "a hopeless flight of the women of the valley, who wanted to escape from a massacre declared by the Vikings during the 15th century".
Two days later the riders start a time trial at Arc et Senans in the Jura, where the visionary architect Ledoux built a royal salt works for Louis XIV in 1771. For a combination of sightseeing and Tour spectating this summer, Arc et Senans would be a good choice.
By coincidence, while the Tour is speeding through the Vosges my cycling buddy and I will be in the same area, inching along the Route des Crêtes on a tour of Alsace; soon to be followed, we hope, by an easier ride along the prettiest wine road in France.
A friend whose hotel in Strasbourg is popular with holiday cyclists tells me we are mad. "Less than 1 per cent" of his clients go anywhere near the mountains, and none weighed down, as I fear we will be, by luggage. Why not stick to the gentle plain? Well, the mountains are an essential component of the beauty of Alsace, and we feel we ought to have a go. Yes, we did once consider ourselves too grown up for the self-improvement kick and the macho masochism of hill cycling. But it sucks you in, does the Tour.
'France on Two Wheels' (Short Books) by Adam Ruck is out now, priced £8.99. For more information, see france2wheels.com.