It started badly. We had dragged ourselves from the huge bed with its fluffy duvet and fine linen at the Hotel du Paris in the old city of Besançon; negotiated the cycle path out of town; bowled along beside the lovely river Doubs for a couple of kilometres, its green forested banks sweeping up the sides of the gorge; when we came to our first hill.
Fifteen minutes of puffing later, and Madame was not pleased. "I want to kill you," she declared. "And Headwater."
It was, it's true, steep. And long – about 1.7 km. I have been a commuter cyclist in London for more than 30 years and have the thighs to prove it. But I could not keep pedalling up this monster.
Sarah, Headwater's charming New Zealander rep, had collected us from the station the previous evening and kitted us out with our bikes – smart 21-gear touring machines with panniers and water bottles. She had warned us about the hill: it was the toughest we would encounter on the eight-day trip. She had also reassuringly disclosed that many previous clients had walked it. "Allow 45 mins to an hour", her handwritten addition to the notes read. We did.
Madame's mood did not improve after we reached the top. We found ourselves in French suburbia – a land of concrete bungalows fronted by gardens with garish flower displays. In 15 minutes, however, we were out of the suburbs and into rolling farmland – fields of stubble and clover, some ploughed, some showing new green shoots – occasionally gagging as we passed tractors scattering slurry.
I was being resolutely cheerful. I was on a bike after all. What experience is there to be had on this earth that is closer to flying? Wheels supply fluidity and grace to the clumsiest grounded human. Alas this was not Madame's experience. At home, her own bike – once a smart racer – has been rusting on its rack, untouched, for years. I had urged her to get some practice in, but apart from a couple of turns round the block, she had resisted. Now she was reaping the consequences. Even on the gentle hills she was having to pause every few hundred yards. "I can't do this," she complained. "I am going to have to leave the bike and take the bus."
We ate lunch – lip-smacking rillettes with fragrant fat tomatoes on a crisp baguette – with our backs to a haystack, surveying a platoon of fluffy white clouds sailing across the sky while the sun warmed our limbs. Even in 22C, it is easy to feel a chill sweeping along on a bike.
As we set off again I thought I noticed a change in Madame's demeanour. Instead of complaining she was now explaining.
"I am letting the lactic acid clear from my legs," she announced as she paused on the next hill.
There was a change, too, in the landscape. We were passing through villages that were rustic; even pretty on many occasions. The smell of freshly cut grass and wood smoke filled our nostrils. We arrived at the edge of a gorge, and plunged down it – a long, thrilling descent to a verdant valley bounded on both sides by ancient forests and limestone cliffs. We stopped and ate a magnificent tarte aux framboises to celebrate. Madame's cheeks were as pink as the patisserie.
This was the Jura we had come looking for – deep gorges, high pastures and fast-flowing rivers squeezed between the Doubs valley at Besançon and the high mountains on the Swiss border. An abundant region inexplicably passed over by the tourist hordes, it is part of Franche-Comté (free country) which has switched allegiances with and against France repeatedly over the centuries. Hence the medieval forts that rule the hilltops.
We ended the day with a dinner of magret avec griottines (duck in kirsch-soaked cherries) and parmentier of beef (Shepherd's pie à la français) at the comfortable La Table de Gustave Hotel in Ornans, admiring the galleried riverfront houses, built just above the water level, while wondering how they had survived centuries of flooding.
Thus was the pattern of our days set. With two days at each hotel (and our luggage carried between them), we spent the first pedalling gamely, uphill and down dale, to our destination and the second was given to exploring, relaxing and "dispersing the lactic acid". The cycling got easier and the countryside more beguiling. Day 3 ended with a marvellous long freewheel looping down into the valley of Salins les Bains, stopping occasionally to admire the spectacular views, the dying sun's rays still warm on our skin.
On Day 4, we spotted our first – and only, as it turned out – foreign tourists – a pleasant Dutch couple. They joined us on the English tour of the spectacular salt works at Salins, a huge underground cavern which has been worked since the 11th century.
At Port Lesney – after a gorgeous sweeping ride on quiet forest roads past trees laden with apples and pretty rural villages bedecked with flowers – the bathers were stretched on the riverbank by the bridge and children were leaping in the fast-flowing water. Alexis and his team at Hotel Edgar were especially solicitous, providing glasses of Macvin and vin de paille – rival vin doux – for me to compare (the Macvin narrowly gets my vote). It was hard to leave Port Lesney – once known as the St Tropez of the Jura. And a stroll before dinner, past its grand houses where the chink of glasses could be heard on vine covered terraces, was a delight.
A lovely gentle ride along the towpath back into the centre of Besançon was followed by a stiff climb – on foot this time – to the monumental citadel that has stood guard over the city for centuries. Gazing over its thick walls down into the fertile valley of the Doubs glimmering in the evening sun, it was easy to see why the residents of this prolific region defended it with such vigour.
Headwater (01606 822688; headwater.com) offers week-long cycling holidays in France from £858pp (tour-only), £909 (self-drive via Eurotunnel) and £1,027 (air-rail). The prices include hotel accommodation with breakfast and some meals, luggage transfers between hotels, bike hire, maps and route notes and round-the-clock support.
Tourism Franche-Comté: en.franche-comte.org