For some cinephiles, reconsidering Krzysztof Kieslowski's Three Colours trilogy is like finding an old photo of yourself in 90s clothes and a 90s haircut. This series of three conceptually interlocking movies – his last work, in fact, before he died following heart surgery in 1996 – was by far Kieslowski's biggest international hit, helped in this country by poster campaigns featuring the luminous stars of each: Juliette Binoche, Julie Delpy and Irène Jacob, a gorgeous young aristocracy of French cinema. The films were co-written by Krzysztof Piesiewicz, a lawyer by training; now a parliamentarian and somewhat conservative figure in Poland.

And, yes, there is a definite touch of dinner-party trendiness that clings to the memory of these movies now, together with a touch of critical doubt, a suspicion that the Three Colours were contrived, over-determined, self-conscious and slow. When the third of these films, Three Colours: Red, was beaten for the Palme D'Or at the 1994 Cannes film festival by Quentin Tarantino's Pulp Fiction, it was a real market correction for a certain type of high arthouse cinema.

Well, the bygone hype that once surrounded the Three Colours may have dated. But watched again sympathetically, the movies themselves stand up, not as the dreamy conversation-pieces of a thousand studenty parties – with blokes pretending to like them to impress their dates – but as an operatic triptych, a dramatic cine-poem of intense strangeness, indulgent and confident, set somewhere which looks like the real world, but isn't.

The trilogy shifts gear from high tragedy to low comedy to intense drama in a world of happenstance and coincidence: it is variously sentimental, grandiose, sexy, eerie and uncanny. The movies are shot through with moments of bizarre black comedy, anxiety and cynicism about Europe itself. With the Eurozone and the European ideal in such crisis, now is an interesting moment to watch the Three Colours again.

The films are Three Colours: Blue (1993), Three Colours: White (1994) and Three Colours: Red (1994), notionally colour-schemed in the manner of the French flag, and – again, notionally – structured around the classic themes of the French republic: liberty, equality and brotherhood. With a little effort, the relevance of each can be detected in each film, but as Kieslowski himself cheerfully conceded, these concepts were there because the production funding was French. The real themes of the trilogy are more disparate, more chaotic, less high-minded, and far more interesting: the unending torture of love, the inevitability of deceit, the fascination of voyeurism and the awful potency of men's fear and loathing of women. To throw everything away, including one's very identity, and start again – that is another powerful, recurrent motif.

They are about entirely different people in different cities, though there are little overlapping, disorientating touches in which the leading character of one film is glimpsed in cameo in another, a technique which effectively points up the artifice of everything that is being presented on screen. (Lucas Belvaux's Trilogy (2002) was similar, but the Venn-diagram overlaps were much closer, and the three films more intimately interconnected.)

What on earth have these people and these stories got to do with each other? At first glance, the final moments of Three Colours: Red would seem to provide an explanation to be applied retrospectively in a backstory "twist", making the Three Colours comparable to Michael Haneke's 71 Fragments of a Chronology of Chance (1994) or indeed Emilio Estevez's Bobby (2006), about the assassination of Robert Kennedy. But at second or third glance, those final moments – that shivering parade of bewildered people on a lifeboat – are quite as perplexing as everything else.

The first film, Blue, begins with a car crash on a remote highway, witnessed by a teenage boy who will later make contact with the only survivor. It is simultaneously the least spectacular and most real car crash imaginable: in an earlier sequence, we have seen brake fluid leaking ominously after a car was speeding along in a bluish haze. Now, in a split-second, we turn with the boy to see the car hit a tree – but with no petrol explosions or drama. It is dream-like, but highly plausible. The fatalities are a renowned composer and his young child; the composer's wife Julie (Juliette Binoche) is badly hurt but still alive. After watching live television coverage of his funeral, immobile on her hospital bed, she finally recovers, sells everything she owns, and lives incognito in Paris. The reason? Is it anguish, grief, rage at fate, and unresolved questions about her late husband's fidelity and his assistant's feelings for her … ?

Not quite. There's something else. An intrusive journalist has made an insinuation which is outrageous, insensitive, but it may well have substance. Has Julie renounced her life because of a falsehood? Does she now live with nothing to do because to continue doing what she did before the accident would be to admit that falsehood to the world?

A year before Kieslowski made this film, the Maastricht treaty had brought the European community into being and the European ideal was a fashionable topic for the political classes in continental Europe, if not the Britain of John Major. In Blue, the composer had been working on a huge, Beethoven's-9th-ish orchestral work to celebrate European union: it is a rather bombastic-sounding piece of music which the audience is nonetheless expected to take seriously. Yet this European anthem appears at disquieting moments. Great, deafening shards of music will crash into scenes with Julie, like traumatic flashbacks, re-awakening Julie to what she is, what she has done. A great chord will announce what looks, bafflingly, like the end of a scene, we fade to black, fade back in – and Julie is still there, still talking, still dealing with her memories. That great chorus of supposed unity is juxtaposed with a drama of dislocation and alienation.

In White (1994), an immigrant Polish hairdresser in Paris, Karol, is being acrimoniously divorced from Dominique (Julie Delpy) because he cannot satisfy her sexually. They were happy enough before they were married, but something about being married, and achieving prosperity in the comparative luxury of France, has unmanned him. Obsessed with his tauntingly gorgeous ex-wife, Karol conceives a plan to get back to Poland, becomes wealthy, and contrives a new scheme to get back at Dominique.

Strangely, this film has one of the biggest laughs I have heard in the cinema, admittedly a cinema with a rarefied clientele. With no money and no passport, Karol plans to get back home by hiding in an enormous trunk and simply being stowed in the hold of a plane as luggage. After a series of misadventures with crooked baggage handlers, his trunk winds up in a grimly snowy garbage dump (that white motif again) and Karol winds up staggering out into this appalling place; he gasps ecstatically: "Jesus! Home at last!" Incidentally, it is possible, though suicidally dangerous, to do what Karol did in this film.

Karol is played by Zbigniew Zamachowski, who I think has a very slight resemblance to Kieslowski himself. Poland itself was not an EU member until 2004, but White dramatises intense Polish feelings that, having jettisoned its communist past, and embraced a market economy, its future was European: Karol's brother says: "We are European now!" But for Karol, this Europe is exemplified by his entrancing, unattainable wife, on whom he felt the need to spy. Her blonde loveliness is explicitly compared, in one shot, to Brigitte Bardot in Le Mépris. In the earlier parts of the film, Karol – poor, lonely, dishevelled Karol – is a rather likable character. But, back in the old country, he starts climbing up the ladder of success, hanging out with gangsters, handling guns, doing dodgy property and currency deals. (Weirdly, Three Colours: White starts looking like an early Emir Kusturica movie.) And Karol becomes a smug, slick-haired, dodgy businessman, vindictive in his need for revenge, and partly, but only partly, softened by the shot of him crying at the end (all three films finish with tears). Kieslowski appears to be asking: is this what Poland wants? Is this what envy of the prosperous European west will lead to?

Red (1994) is arguably the strangest of the three. Irène Jacob is unsettlingly like Juliette Binoche physically; her presence in the last film bookends Binoche's like a doppelganger, as in Kieslowski's Double Life of Véronique. (Although it has to be said that Binoche is a far superior performer.) She plays Valentine, a student and part-time fashion model in Geneva, plagued by calls from her controlling and jealous boyfriend in England. A quirk of fate causes her to call upon a cantankerous and retired judge, played by Jean-Louis Trintignant, an aggressive malcontent with an illegal hobby, which – to the judge's evident contempt – Valentine tries vainly to nip in the bud. But through the same tangled, contrived workings of fate, the judge turns out to have a contact with a neighbour of Valentine's, and one of his neighbours may have a connection with Valentine's unhappy younger brother. They become close. An ad shoot for bubble gum, starring Valentine, results in a massive billboard whose image is supernaturally echoed at the end of the film. Wittily, and ingeniously, the length of time dramatised in the film is the length of the ad campaign: the huge image is put up at a street intersection at the beginning of the film, and taken down by workmen at the end.

Remembered dreams are an important theme in Kieslowski, and importantly, the judge tells Valentine that he has had a dream about her. The dream is never shown on screen, merely recalled, but it is perhaps the most poignant part of the trilogy: a dream of Valentine's future, which she finds moving, for reasons she cannot explain.

The Three Colours Trilogy was much swooned-over at the time for its ambient stylishness and sexiness, but I think this is the aspect which dates it. Much more interesting is to see it as an exotic hothouse flower, or perhaps a gigantic, puzzling three-part installation, resplendent with its own self-confident strangeness and beauty. Just to watch one single film deprives you of the flavour. Perhaps it is best not taken entirely seriously, you have to see the drama, even at its most exalted or tragic or erotic, as something satirical. Perhaps it is best, heretically, to watch the films out of sequence. Work outwards from White (my favourite of the three) the trilogy's black comic centre, and savour Karol staggering joyfully out of his manky suitcase, euphorically re-born with nothing.

• This article was amended on 14 November 2011. The original said Kieslowski died of cancer in 1995. This has been corrected.