Undeterred, two days later my wife and I had tracked down a tiny boatyard reeking of wood shavings and creosote at Mareuil, the only workshop on the river still crafting traditional gabarots by hand from oak, chestnut and alder.
We had never taken our children on a boating holiday before. But the Dordogne seemed ideal for beginners: it is slow-moving in summer and motorboats are prohibited on all but a tiny stretch. We could not rent a gabarot so we bought one, complete with paddles and wooden bailer. The Fr2,200 ( pounds 275) looked a modest investment when we knew we could sell the boat back to the workshop for about Fr1,500 at the end of the trip.
At Beaulieu-sur-Dordogne we tied down the watertight drum containing our belongings, slipped our sleek 15ft craft into the water and gingerly pushed away from the bank. As we did so, nine hours of noisy quarrelling in the back of the car abruptly died away, its place taken by the quiet gurgle of water lapping against the sides of the boat. Our children sat hushed in the prow, eagerly watching out for tufted grebe, the iridescent flash of a passing kingfisher and turning silently to point out a grey heron standing motionless on the riverbank.
Although at first it seemed alarmingly low in the water, the gabarot was remarkably stable. There was plenty of room for our camping equipment and pots and pans in the stern, as well as bottles of wine, a fishing rod and a picnic hamper.
We all wore lifejackets, even when the surface of the Dordogne was as calm as a millpond: buckling on a lifejacket should be as automatic on the water as wearing a safety belt is in a car. The danger, we were told, was less of drowning than of falling overboard and knocking oneself unconscious on a rock. 'At least with a lifejacket on you'll float and we can fish you out of the water,' a fireman assured us jovially in a bar at Beaulieu.
Steering a gabarot is something of an art, but my wife and I soon handed the paddles to our children, aged 13 and 14, who quickly mastered the technique and took us smoothly downstream with all the skill and pride of professional boatmen. Only once or twice did we have to leap for the paddles when the boat began to drift sideways down some rapids. On the whole, though, ours was a stately and dignified descent of the river.
In the afternoons we would look out for an official campsite or a little grassy clearing beside the river where we could pitch our tent unobserved. Whether carrying tents ashore, collecting branches for a campfire or checking that our gabarot was securely moored for the night, our children were always active and enthusiastic, determined we should not get bored with the whole thing.
At the end of the day, unaccustomed to such quantities of fresh air and tired out by the exercise of paddling, we were in our tents by nine o'clock and asleep five minutes later. Nights passed uneventfully except for the call of an owl, the croak of a frog or the splash of a fish in the river.
When we woke in the morning we generally made our way downstream to the next village for a breakfast of freshly baked croissants and cafes au lait. Being on the river for an hour before breakfast, with the mist rising through the poplars in the early morning sun, was an experience not to be missed.
Our arrival by boat at a village never failed to cause a stir. For some we were 'les anglais sportifs', for others part of the new wave of English laying claim to the old Plantagenet domains of Aquitaine. Old riverhands crowded round to tap the hull of our gabarot, impressed by her craftsmanship, and to tell us stories about the old way of life on the river. News of our progress seemed to precede us downstream and twice in a bar we found a round of drinks had been bought for us. At La Roque-Gageac an English tourist, who had seen our approach from his hotel, appeared breathless on the quay, camcorder in hand, and began interviewing us as we came ashore.
Every few miles we came across either a riverside village with small family-run hotels or a delightful shady campsite. Finding accommodation was never a problem. The difficulty was in deciding where to stay: everywhere looked so inviting. Of the many delightful hotels, our favourite was Les Falaises at Gluges, an old Perigourdin auberge nestling beneath overhanging cliffs streaked black and gold. While my wife and I sat cradling huge bowls of coffee on the terrace overlooking the river, our children explored the cliffs honeycombed with caves and ancient troglodytic dwellings.
We tied up to visit the blood-red fortress of Castelnau, the stalactite-filled caves of Lacave and the elegant Chateau de la Treyne, dating back to the Renaissance and once the home of the black American cabaret singer Josephine Baker. One day we abandoned our boat to walk over the hills to Les-Eyzies, home to the earliest prehistoric finds in Europe. On the way back we found the king of mushrooms, boletus edulis, in dense chestnut woods and cooked an omelette aux cepes worthy of a Michelin star.
The most beautiful part of the Dordogne lay between Souillac and the dreamlike village of Limeuil, where every house was a jewel of golden stone. Each bend in the river revealed another medieval chateau perched precipitously on a rock above the water: Beynac, Fayrac, Fenelon, Montfort. As our children were determined to visit them all, my wife and I took it in turns to sunbathe beside the boat while the other one climbed dutifully up the steep hillsides. The most rewarding was the Chateau de Castelnaud (not to be confused with Castelnau), with its reconstructions of the great weapons of medieval warfare - huge stone-slinging devices made from wood, leather and stone.
One of the great advantages of heading downstream was that the river did all the work. While our children piloted us effortlessly, my wife lay back and read her book in the sunshine and I idly toyed with our fishing rod, trailing a red plastic maggot behind the boat. One day I reeled in a 10in brown trout, much to my family's astonishment. Minutes later our son caught a second and we fried them over the campfire with butter and wild chives.
Travelling by gabarot also opened doors for us, being a starting point for many conversations about the history of the river and the region. The Dordogne, we learnt, had once been a thriving waterway, busy with flat-bottomed gabares bringing wood from the Auvergne and wine from the middle Dordogne downstream to the barrel makers and wine merchants of Libourne and Bordeaux. Virtually every village still has its cobbled quay. Abandoned after the railway put an end to the river traffic in the 1890s, these overgrown quays were ideal places for tranquil lunchtime picnics and leisurely siestas.
Undeterred by Arctic temperatures, our children swam in the sheltered pools of the Dordogne and occasionally beside the boat as we drifted downstream. The closest we came to disaster was when our son scrambled back in over the side one day and came within an inch of capsizing the boat.
When the locals in a bar in Ste-Foy-la- Grande discovered we had arrived from Beaulieu by gabarot, a man was sent to fetch the mayor. A rotund, jovial, red- faced man, the author of two books on the river traffic of the Dordogne, he abandoned his office to give us a personal guided tour of his beloved river museum. Our journey was, he assured us, 'une belle aventure'.
Further downstream we came to the vineyards of St Emilion and Bordeaux and visited the great Chateau de Monbazillac for a free degustation of the finest of all French dessert wines. Still further down was Montaigne's chateau and Castillon-la-Bataille, the site of the defeat in 1453 of the English army in the last great engagement of the Hundred Years War. Arriving at these sites by boat or on foot brought them to life: our holiday was a history, geography, natural history and French lesson combined with a dash of adventure training.
When we walked up to visit a village or chateau we left everything in the boat except our valuables, and in two weeks had only one minor theft: a few tins of tuna, some cheese and two bottles of St Emilion. Tent, sleeping bags, lifejackets and clothes had not been touched. It was, we reckoned, a quintessentially French theft.
On the water we had the best of both worlds: all the beauty of the riverside villages and car-free bliss. After two weeks we were tanned, healthy and fit, and the sound of children quarrelling was but a distant memory. By the time we reached our final destination at Libourne we had only one desire: to do the whole thing all over again.