At first, I thought it was a coat in the water – a big black coat puffed up with air, floating down the Seine in the early spring sunshine. It was perhaps 20 yards away when I realised that it wasn’t a coat. It was a girl in the water.

I have learned – as I’ll explain, this was not the first time I’d encountered a woman floating in a river – to act as quickly as possible. To keep moving and keep the options open. So I started taking off my clothes and shoes while trying to think. I noted that she wasn’t far off. That she looked quite small. And that the water looked a bit wintry – swollen and muddy – but not dangerous. In the end it comes down to Can I do this? By now my girlfriend was on the phone to the police and I thought Yes, I can. I slipped into the water, pushed off from the quay into the current, and in what felt like seconds I was with her. The hand that reached out to me as I approached was disturbingly cold. But I pulled her to me and got her under the arms. It was astonishingly easy to tow her to the bank.

On the quay, we stripped off her wet coat – she felt like something on a slab – and covered her in my dry one. We didn’t know what to do. Her hoodie looked cheap and her Afro hair was unkempt. She might have been 12, maybe 14. I told her my name and asked for hers, repeatedly, but she didn’t reply. She looked through me. Absurdly, a Batobus floated by and I felt everyone stare at me in my white underwear. Then sirens approached from the road and boats came roaring up the river and the riverbank filled with people in heavy nylon uniforms. I dressed surreptitiously, becoming just another bystander, albeit with damp hair and a ball of wet clothes in my bag.

The police weren’t interested. To them it was the same old story. Except that, as they carried the girl into the ambulance, one of them called me over. The girl was lying on a stretcher, wrapped in a blanket, and he reached for a medallion hanging around her neck, showing to me the two words embossed on it: Sourde-Muette.

It means deaf-mute.

For a long time, I believed that this incident had made no impact on my life, apart from giving birth to some uneasy dreams. It was a momentary contact, a brief immersion. Nothing had been at stake for me, I’d had time to judge the risk, and my intervention hadn’t been physically demanding. The incident just swirled on by, leaving hardly a surface ripple. There were some unanswered questions, which I mostly pushed to the back of my mind. Did she recover? How long would that coat have held air? Did she fall or did she jump, or – and I don’t like thinking about this – was she pushed? I never found out her name.

The questions wouldn’t quite go away, and neither would the dreams. They still well up, full of insecurity and displacement – and water. Sometimes, I’m in a violent Himalayan river, or it’s Venice and I’m crossing and recrossing a dark canal. Only last night, as I write this, I was caught by the tide on a slippery rock, my dream-self too scared to swim to safety and too tongue-tied to call for help. Strange how anxiety dreams are so often characterised by a wretched inarticulacy.

Perhaps this is not really an ethical problem, but a narrative one

I am still bothered by the question of whether I did the right thing. Because if the girl had jumped – and I think that perhaps she did jump – then I can’t help thinking that far from ‘saving’ her I might have been condemning her to more of the suffering that, presumably, she was trying to escape. No one asked me to intervene. She didn’t. And yet to have watched her float by would have been monstrous.

Perhaps, as a friend suggested, this is not really an ethical problem, but a narrative one. Worrying as I do, he suggested, is a displacement activity, a way to try to create meaning where there isn’t any because I do not know the end of the story – or, come to that, the beginning of the story. The incident doesn’t go anywhere or mean anything. The girl appeared on the current and vanished in an ambulance, like a bedraggled Bede’s sparrow.

Recently, I’ve tried for the first time to find out more. I had taken a photo earlier on that day I’d pulled the girl out of the river, and of course all digital photographs are time-stamped, so I had something to search for. I typed in the bare bones – ‘girl drowning Seine’ – along with the date. April 2006. The only story that came up, however, was much stranger than anything I’d been seeking; about a young woman who’d drowned in the 19th century – and whose face had afterwards become an artistic talisman.

She is known as L’Inconnue de la Seine, or the Unknown Woman of the Seine. She drowned in the 1880s (or so the story goes), and was taken to the Paris morgue. There, her extraordinary, beatific smile so amazed a medical assistant that he made a death mask in plaster. The mask was then reproduced in the thousands, becoming an eroticised cult-object for decadents, modernists and artists of all kinds. Chiefly male ones. The novelist Louis-Ferdinand Céline had a copy. Rainer Maria Rilke wrote about seeing her in a workshop every day, in his novel The Notebooks of Malte Laurids Brigge (1910). Vladimir Nabokov, in a 1934 poem, begged her to ‘reply with a posthumous half-smile of your charmed gypsum lips’. Albert Camus wrote that his plaster-cast version looked like a drowned Mona Lisa.

I worried that I might frighten her, that I might be the very thing she was escaping

Then I read about the turn-of-the-century writer Richard le Gallienne, best known today for his brief affair with Oscar Wilde, and his creepy, overripe novella The Worshipper of the Image (1900). It centres on a poet who finds a mask of the Inconnue in a sculptor’s shop and falls obsessively in love with it. He calls her Silencieux. (Gallienne adds in an awkward footnote that he knows it should really be silencieuse, in the feminine.) The name means ‘silent one’.

I felt uncomfortable reading all this. All those men gazing ardently and morbidly at a drowned woman’s face. A silenced woman onto whom anything could be projected – and was. My encounter with my own Inconnue could not have been less erotic. I felt repelled by her closeness to death; I remember forcing myself not to recoil from the touch of her hand. But, then again, was the incident entirely sexless? I know that I was acutely conscious of my maleness as I knelt over her on the quay. I worried that I might frighten her, that I might be the very thing she was escaping. I worried, above all, that I should not be taking off any of her clothes.

The story of the Inconnue has a weird coda. Pursuing the story online, I came across the Norwegian doll-maker Asmund Laerdal, who saved his two-year-old son Tore from drowning in 1955. Later, he created the first soft-plastic dummy for training resuscitation techniques, choosing to model the dummy’s face on that of a smiling mask he’d remembered hanging on a wall in a relative’s house. It was the Inconnue. His choice was deliberate. As a study on ‘The Resuscitation Greats’ (2002) notes, Laerdal thought ‘men would be loath to practise mouth-to-mouth ventilation on men’, and that the Inconnue’s ‘wistful, enigmatic and peaceful countenance’ made her ‘beautiful but not sexy’. Laerdal’s dummy was an unexpected success. As a BBC article puts it, ‘if you’re one of the 300 million people who’s been trained in CPR, you’ve almost certainly had your lips pressed to the Inconnue’s.’

Laerdal’s experience with his son led to a life-saving invention, while my encounter with the girl in the Seine had no such impact, not even on me. Although, when I hold it up against another, earlier experience, I think it has led to an insight, or at least a realisation.

I mentioned that when I saw that girl in the river it was not the first time. Ten years before, I was walking around Geneva in the middle of the night – I had a dawn flight out of the city and no money – when I saw a woman in the Rhône, where it pours out of the lake. She was huge, riding oddly high in the black water, her dress ballooning around her. She was shouting ‘Au secours!’ Unambiguous. I started to run to keep pace with her. Dropped my rucksack, my coat, my jumper, and called for help. I was desperately trying to decide Can I do this? I was a weak swimmer, then. The water was so dark, the woman so large and I had no idea what lay downstream. I was afraid. But I was running and shouting and no one was coming. I remember thinking I have to go in as a car skidded to a halt beside me and two Swiss policemen leapt out and dived without hesitation into the water.

I retraced my steps along the riverbank, picking up my clothes. Later, at home, I got swimming lessons. I also read up on the 10-80-10 theory. Supposedly, in a crisis, 10 per cent of people panic, 80 per cent are bewildered and frozen, and 10 per cent act with reason and resolve. I wanted to be in the third group next time. I wanted to be the kind of person who keeps his head but does something.

That thinking undoubtedly helped me get in the water in Paris. But this isn’t the insight I was referring to. Rather, I have come to think that, on the whole, it is better to regret having done something than to regret not having done it. It’s better to be involved. I find it a useful mantra when confronted with doubt, and when responding to opportunities for adventure. Also, when responding to other people’s grief or sadness, it’s always best to say something. You will make mistakes, but the quality of any regret that follows is more bearable when they are mistakes of commission rather than omission. I have to live with the thought that the unknown girl’s silent life may have been intolerable to her, and all I did was make it longer. But I can live with that. I’m not sure I could have lived with myself, though, if I’d stayed on the riverbank, watching.