My grandson and I are reprising the 1968 film The Swimmer. Burt Lancaster is an advertising executive at a pool party who attempts to swim eight miles home via his affluent Connecticut neighbourhood’s outdoor swimming pools. We don’t have a pool, but our friends are generous with offers to use theirs. Our aim is to take advantage of these offers by swimming in a different pool every day and working our way through the expat society of this remote part of the Provence.

It’s Oscar’s first trip abroad; he is staying for a fortnight. Today was day four. The effect of the contrast in his plastic mind between a flat above a hairdressers in Newton Abbot in Devon and a daily succession of private pools in a 42°C heatwave in the hills of Provence must be very great. He is red in the face but so far appears to be taking it all in his stride. The enormous, martial, intelligent ants have impressed him so far; also this one particular yellow-and-black lizard, inscrutable and pacific, which he persecutes daily without mercy until it loses its rag and attacks him. Once he brought it into the house with its toothless mouth clamped on the end of a stick.

On his first morning here we packed our Speedos and swam in a pool in front of a magnificent old pantiled Provençal villa. The owners were out, but had kindly left us a glass jug of iced water on a tray with two glasses on a filigree-wrought iron table. The jug was a masterpiece of 1950s design with a curving lip to hold back the ice cubes as you pour. A beautifully elaborate lace doily weighted with coloured beads was draped across the top to keep the flies off. The pair of upturned water glasses were heavy and stylish in their rustic simplicity. As we swam in the cold pellucid blue, all we could hear, above the slop of the water, was the perpetual quick-step marimba shuffle of the cigales in the shade trees, punctuated by the sonorous clung of a single church bell from the monastery on the hill. We floated on our backs and saw a Bonelli’s eagle on the wing in the air above us. ‘What do you think of this then?’ I said.

The next day’s pool belonged to a foreign television correspondent who once lost a kidney to a Serbian sniper, and his Russian filmmaker wife. You enter the property through a gate in the village and find yourself unexpectedly in the countryside. The house is a late 18th-century former mayor’s residence in the shade of a magnificent old Aleppo pine. Captured Allied airmen were confined in the cellar by the Nazis during the war. We were welcomed and kissed by the filmmaker wearing a ruby dress and matching ruby slippers, and by Mary the cocker spaniel. The foreign correspondent was away in the Middle East. She led us to the pool, advised us to keep our straw hats on even in the water and left us to it. This pool was secluded on three sides by mature lavender bushes. The fourth side overlooked a secluded valley. The air temperature was a dizzying 42°C; the pale green water was 25 and chilly. I felt it my duty to tell Oscar that not everybody here has houses and pools like this.

The next day we swam in the pool of a British TV presenter. I used to tell Oscar he was famous. Then, he didn’t know what the word meant, and I’m not sure that he does now at the grand old age of seven. ‘And this guy is even more famous than you,’ I said. The sun was so fierce we stayed in the pool for the best part of the afternoon. The TV presenter and his wife and young son came in too. This pool was notable for the availability of the most advanced and powerful pump-action water pistols on the market, and comfortable snorkelling masks and goggles, and flippers, and a shark-fin buoyancy aid, and best of all, as far as Grandad was concerned, an outdoor refrigerated bar, packed solid with ice-cold Leffe beer, and a sort of bedouin tent to one side with comfortable sofas on which to drink them.

Tomorrow’s pool is an infinity pool belonging to a comedian, I told Oscar last night after I’d said his prayers under the wobbling ceiling fan. What’s an infinity pool, he said? I explained the concept of an infinity pool. And what’s a comedian, he said? Someone who makes you laugh, I said. He was thinking about this, then his eyelids closed and stayed closed and he was asleep.