The Sexual Life of Cathérine M, Cathérine Millet, translated by Adriana Hunter

This wild erotic memoir puts Deborah Levy in mind of the spirit more than the flesh

Rammed up against a wall by the gates of Paris, Cathérine Millet, curator and art critic, takes off her raincoat and has sex with a number of men. All the while, as agreed between the couple, her long-time lover watches her "nailed by their pricks, like a butterfly".

Rammed up against a wall by the gates of Paris, Cathérine Millet, curator and art critic, takes off her raincoat and has sex with a number of men. All the while, as agreed between the couple, her long-time lover watches her "nailed by their pricks, like a butterfly".

The most interesting part of Millet's memoir of her sexual encounters with strangers and groups of strangers is that she does not present herself as a seductress. Almost from the moment she loses both her virginity and her Catholic faith at 18, she is completely sexually available to men, preferably lots of them at the same time. More confident naked than clothed, her body seems to become a sort of machine as she attempts to fill the "vacancy" left by the death of God. It is as if the enigmatic Cathérine has stepped out of the novels of Georges Bataille or the films of Luis Buñuel, and into the car parks, offices, museums and singles bars of contemporary Paris, to prove once again that Catholicism and filthy sex go together like salt beef and rye.

The Sexual Life of Cathérine M, with its ironic homage to The Story of O, is really existential pornography – something the French seem to do so much better than the rest of us who are checking in to the Holiday Inn this weekend. Millet's achievement is that she curates or, more accurately, catalogues her sexual adventures with no sense of shame or remorse. She writes about sex as if it were an autopsy, finding time between positions and partners to throw in the odd philosophical insight on landscape, atmosphere, time, space, dirt and numbers.

In cool, spare and formal prose, she states that her place in the world is "not so much amongst the women, facing the men, but alongside the men". I think that what she means here is that her partial sexual taste is for nameless, loveless, faceless sex – although in interviews she has said that she thinks women attach less importance to the sexual act than men do.

Unlike the erotic short stories of Anaïs Nin, which nearly always involve a dance between men and women, the latter revealing, concealing, playfully luring the object of desire into their perfumed webs, there is very little narrative foreplay in Millet's descriptions of her encounters. More interested in sensation than emotion, she lets the nerve endings on the surface of her skin do the talking. When she's aroused, her lips go cold – an observation that excited me more than the eye-watering positions she describes so graphically, and often boringly. In fact, if there is anything that is taboo in Millet's uninhibited memoir, it is emotion. The only thing that is private about her is her inner life.

Yet if her compelling, cool and stylish memoir is about the life of a female body, it is also about a disembodied female body, a number of orifices, genitalia, limbs. In a sense she has less in common with the poetic sadism of de Sade than the often comic masochism of fakirs: those who do weird stuff to get to extreme spiritual states, walking barefoot on hot coals, lying on shards of glass, being buried alive, holding their arms above their head for years at a stretch.

This is supposed to be to do with bodily privation rather than pleasure, but there is also privation at the heart of this sexual memoir. Millet, in my view, does not come across as a transgressive woman who reverses "the classical power game in which men take the lead and women submit", as some critics have asserted.

She comes across as unloved, numb, passive, hungry for male approval, exhausted rather than energised by fantasy. If there is anything transgressive about Millet's memoir it is her admirable lack of disgust at the human body and her refusal to psychoanalyse her desires when she knows full well we want her to.

I respect her refusal to do so because no one ever asks men – such as Henry Miller, never mind Peter Stringfellow – to give us a Freudian take on their sexual appetites. Yet this refusal leaves a hole, and this of course might be the point, at the centre of her story.

What is it we want to know when we read her book? Insatiably to pursue sex for its own sake, and declare it has no other meaning, is a stance I just don't find at all convincing. It would be like saying someone pursues anger for its own sake and it has no other meaning. I'm thinking of Millet, swinging in 1968, refusing to partake in the bourgeois institutions of marriage, monogamy and children, hanging out with the philandering guys of that generation, apparently feeling empowered, expressed and free. In my experience, all those guys eventually married, had babies and suddenly discovered they needed some rather stern sexual boundaries with their partner.

So where does that leave those brave gorgeous girls who wanted to line up alongside the boys? In Millet's case, with a husband who organises and enjoys watching her sexual adventures with other men. Is this a match made in heaven or in hell?

Millet does briefly tell us that, unlike so many girls, she had no idealised notion of love, no expectations of what it might mean. Now that is really interesting, and its examination would have given this strangely detached memoir a bit more substance. But I will say one thing: Cathérine Millet has more fun at the dentist than I've ever had. If you want to know more about how to liven up root canal treatment, buy this book immediately.

Deborah Levy's 'Plays: 1' are published by Methuen.