It’s fascinating to watch a famous film actor up close, especially one as alluring as Juliette Binoche. The first of her films I saw was Philip Kaufman’s adaptation of Milan Kundera’s The Unbearable Lightness of Being (1988). Daniel Day-Lewis, her co-star, played a handsome Czech brain surgeon and libertine whose catchphrase was: “Take off your clothes.” I was an adolescent studying philosophy at the time and was naturally thrilled by the film’s combination of sex, smart talk and metaphysics.

I waited a long time before I saw Binoche in the flesh, as it were – in the avant-garde dance drama In-I, in which she performed alongside the British choreographer Akram Khan at the National Theatre in 2008. In-I was a curiosity, a study in erotic obsession, to which Binoche seemed to give herself completely in what was an exhausting and sweat-drenched performance (and that was just for those of us watching open-mouthed in the audience).

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Binoche is now 51 and still beautiful. She has thick, dark hair, wide cheekbones and pale skin. She is shorter than you imagine and has muscular, gym-toned arms. In In-I she hurled herself around the stage as she and Khan took us through the various stages of a relationship, from mutual infatuation to final desolation. As they pulled each other into a series of ever more tortured embraces, one was reminded of Binoche’s tangled (and preposterous) sex scenes with Jeremy Irons in Louis Malle’s film adaptation of Damage.

At various times, in the Belgian director Ivo van Hove’s production of Antigone, Binoche writhes on the stage in an ecstasy of torment. She falls to her knees as she rages and curses. She pulls herself into the foetal position. She even drags herself around on her bottom, as if she has forgotten how to walk. Hers is an intensely physical performance. Yet she is equally capable of moments of repose, such as when she sits on the edge of the stage, her legs dangling, as if unaware that we are so close, and watching her.

In the Canadian poet Anne Carson’s new English translation of Sophocles’s 2,500-year-old play, Antigone, the daughter of Oedipus, speaks the opening line to her sister, Ismene: “We come out of the dark.” Projected behind them on a large scree is a barren, near-desert landscape through which you imagine them wandering. Binoche wears loose-fitting contemporary black clothes and, in spite of her opening pronouncement, never really enters the light – because she is doomed from the moment she chooses to defy her uncle, Kreon, the new autocratic ruler of Thebes who is striving to impose order in a cursed land.

The central problem of Antigone is that much has happened before the play even begins, and to understand it one need to know the story of Oedipus, Greek tragedy’s original sinner. The land of Thebes has been ravaged by misfortune and Oedipus’s feuding sons, Polyneikes and Eteokles, have been killed fighting each other in a civil war. Kreon (a bald-headed and vigorous Patrick O’Kane) considers Polyneikes to have been a traitor and will not allow him the dignity of a burial, preferring to leave his body to rot. Antigone refuses to accept Kreon’s edict. She demands that her brother be buried rather than left to become “sweet sorry­meat for the little lusts of birds”.

Binoche’s Antigone is easier to respect than to pity and, for some reason, one never really feels the pathos of her struggles. Antigone, her sister says, is “someone in love with the impossible”. Binoche captures well her righteousness and implacability. Her foolhardiness, too. She does not fear death. Nor does she recognise the authority of her uncle or indeed the secular state. In a pagan world of gods and strange prophecies, she is unreachable in her isolation, imprisoned by Kreon but free to take her own life, which she does in a final act of defiance.

The production experiments with multi­media effects, not all of them successful; at times, it can feel a bit like you are watching the latest shortlisted piece for the Turner Prize. Yet the final scene, with Antigone dead and Kreon stricken by remorse, is perhaps the best. For the first time, the combination of music (before this, mostly electronic ambient), video images (often of blurred modern London street scenes) and stage performance fuses powerfully. The pace quickens. The Velvet Underground’s “Heroin” blasts out and, on the large screen, we see Antigone lying dead as Kreon stands by her side. He lifts a white sheet and uses it gently to cover her face. In death Antigone seems serene. It is the living who must go on suffering.