Our third day in Paris started with a near-drowning. We were sitting in bed having our first coffee of the day when we heard splashing outside the boat. It sounded like someone was swimming right beside Liberty, but you'd have to be mad to swim in the marina water. And yet we could definitely hear vigorous splashing and bubbling.

We went on deck in our dressing gowns and leaned over the rail. There on the swim platform, having just managed to drag itself to safety, was a very wet and bedraggled tabby cat. He looked up at us and gave the most heart-wrenching meow you've ever heard. You don't need to speak Cat to know it meant 'I fell in!' And looking at the drenched animal we didn't need to be told.

The cat repeated its plight loudly, in fact with such volume its howls echoed around the marina and we were worried lest someone thought we were abusing the poor animal. I climbed down the ladder to the platform and tried to lift the soggy moggy but he kept digging his claws into the rope that was coiled there, probably fearing I was going to throw him back in.

I tugged, he clung, I tugged more, he howled louder, and then I realised I was actually standing on his tail, so I was actually trying to lift him while keeping him trapped, and trying not to fall in the water myself. Between the two of us we were making a dog's breakfast of the whole affair. It was a tragic yet comical situation. Liz went to get the camera but couldn't find it. She returned instead with something far more appropriate - a towel - and having de-clung the cat and released its tail I passed the dripping feline up to her.

She had no sooner got him in the towel than he leapt away and disappeared, no doubt back to wherever he lived, to shake himself dry and maybe lie low for a while to hide his acute embarrassment - and count how many of his lives he had left.

Shame we didn't get a photo though - the image would be the sort of thing you'd use on a poster beside a lock, which would have written underneath, 'Always, ALWAYS, wear a life jacket.'

Having saved a life we then took the Metro to see some still lifes, in Rodin's garden. It was lovely warm sunny weather for wandering around the gorgeous garden in the grounds of the hotel where he lived in his dotage and which is now a museum to his life and works.

Rodin seemed to have spent much of his career battling with others, some of whom thought he was a fraud and some who simply didn't like his commissioned works when they were completed. He seems to be the perfect image of the tortured artist, and many of his subjects seem somewhat at odds with the world too.

The Thinker, for example. ponders on his plinth amid cone-shaped shrubbery, tourists striking a similar pose in front for photos. (Seriously; can't they think of something less clichéd? It's like those people who pose themselves pushing against the Leaning Tower of Pisa to 'stop it falling over'. Yawn.) The statue of The Thinker is actually Dante contemplating hell and mankind's fall - serious thoughts indeed - though looking at him I suspected he was actually thinking, 'Can't these bloody tourists come up with something new for a change?!'

Rodin died in 1917, apparently ending his days not making bronze statues but instead sketching attractive young naked women. Finally I have a plan for my retirement...

We then went to the Parc des Buttes Chaumont which we'd read about online. (It pays to Google phrases such as 'Hidden Paris', 'Secret Paris', etc, to see what comes up. One suggestion was to take a tour of the Paris sewers, but we decided to save that for another visit...)

Anyway, the park is an old quarry in the 19th arrondissement, which has been landscaped with sloping lawns, lots of trees, snaking paths, a lake, streams and even a waterfall. We saved exploring fully until we'd had our picnic lunch on a sunny grassy slope.

There was another couple sitting on the bank not far from us who looked like something out of a Woody Allen movie - him looking Jewish with rimless glasses, beard and dark hat, and her dressed in almost 1920s clothing. They were drinking wine, but he seemed uneasy about it and kept looking round at us perched further up the hill, either hoping for a nod of approval or that we hadn't seen the alcohol. We generated an air of nonchalance, and sipped from our own wine glasses in the hope it sent a message of support. L'chaim!

We then set off to explore this 'secret' piece if Paris, but were a bit underwhelmed at first as it seemed just like many other parks. But it was only because the entrance we'd come in was at the opposite end of the quarry bit, and once we'd discovered the park proper it was lovely, though hardly a secret given the number of people there; hundreds... singles, couples, groups, families, picnics, sunbathers, and - of course - dogs. Always dogs.

We found the lake, and a grotto, streams, a cave, the waterfall, the snaking paths, the classical gazebo on the hill from where you can get good views over Paris. The old quarried cliffs added to the drama of the landscape, and it was easy to forget you were in the centre of the French capital. It's a little piece of paradise, and while not as secret or hidden as the web might suggest, is still worth a visit.

Later in the evening we were back on the boat and the woman who had found Liz's stollen wallet, Anne, came on board to return the property. Her English was way better than our French, and we chatted for a long time. We are very grateful to her for noticing the wallet even if the thief had already taken the credit cards and driver's licence. It's the licence that worries us most as it can be used as fake ID to open accounts and which, when they fall overdue for payment, could result in Liz getting a bad credit rating. Identity theft is a serious matter. We are keeping our fingers crossed the thief doesn't have any English connections to fence the licence to.

Next day we headed for the Arc de Triomphe - by driverless train. We wondered how the Metro people knew where their trains were without drivers, or how fast they were going, or when to stop them, but we assumed it was all done from a central control room and operated in the same way as a model railway. Maybe the controller is a nine year-old. Whatever, it worked, and without a driver's compartment up front we had a great view of the underground journey as we were swept along the shining rails, the tunnel lights rushing by and brightly-lit stations emerging from the darkness ahead. Not such a great view for the unemployed train drivers though.

We slogged our way up the more than 280-step spiral staircase at the Arc de Triomphe, to finally emerge at the top in brilliantly sunny weather. Gorgeous - and great views over Paris. We were mesmerised by the traffic jockeying for position below as it flowed bacteria-like around the arch, braking, starting, pausing, slowing, speeding and - in one instance - colliding, though it was a very minor bump with no fisticuffs or thrown gauntlets. Shame, because we could have recommended a great park as the ideal location for pistols at dawn.

Everyone somehow seemed to know what to do, despite the lack of road markings or traffic lights, and it all seemed to be based on giving way to the right. Right? Maybe.

We strolled down the Avenue de Champs Élysées, stopping in at the Mercedes shop (as you do) to ogle some vintage Merc sports cars. They were absolutely pristine - in showroom condition - and had obviously never been driven round the Arc de T.

There was all manner of three-pronged star merchandise for sale too, from polo shirts and belt buckles to model cars and cigarette lighters. I sprayed on some Mercedes man-smell stuff but was disappointed to find it didn't reek of diesel. Needless to say we didn't buy a car, model or otherwise.

Maybe it's because the Champs Élysées is a posh avenue, but the Metro stations don't have any big signs showing where they are. Instead you just stumble across steps disappearing into the ground every now and then, and only then do you see a discreet 'Metro' carved into the stonework. But once we'd found a station we took the train and had a picnic lunch on the slopes of Montmartre with the cathedral as our backdrop, gleaming white in the sun. There were many many people, including a wedding couple being photographed on the steps, though it's going to take someone a lot of time to Photoshop the hundreds of tourists out of the frame.

Liz and I had both been to Montmartre before so didn't feel the need to go inside, and instead we strolled around the artists' quarter where artists were busy painting, sketching and otherwise rendering their sitting subjects, or depicting famous Parisian scenes. Some of them were absolutely fantastic, but we decided not to have our portraits done. Instead we bought a monochromatic water colour of boats on the Seine by a nice young man who didn't have much English. Liz was especially taken with the picture, as I was, and so we made his day by not haggling too much.

And then, a most un-touristy thing to do - we strolled to the curtain and material shops as we had originally planned to do on Pickpocket Day. There are a few streets just at the bottom of the Montmartre steps with multiple stores selling all sorts of material from faux furs and pinstripes to the finest linens and cottons. This was haberdashery heaven, and we finally found what we'd been looking for for our new kitchen and lounge curtains, yay! We will even be able to say, 'But of course we had to go to Paris to find what we wanted, darling!' (Yes, we live in a material world)

Even better, this time we managed to avoid the pickpockets.