Nearly 40 years after “Band of Outsiders” and “A Woman Is a Woman” double-dosed the 2nd New York Film Festival, Jean-Luc Godard continues to astonish and annoy in equal measure. I’m sure the cranky maitre wouldn’t have it any other way; obstinance is his air, solitude his shelter, resistance his light. The day a new Godard film ruffles no feathers is the day Oprah picks Pound’s “Cantos” for her book club.

His latest, “Notre Musique,” which screens tonight in the festival before opening at Film Forum on November 24, is either a sublime swan song by one of the great artists of the 20th century or the spurious free association of a postmodern crank, depending on whom you ask. As an incorrigible Godardist myself, I’d call it one of the two supreme masterpieces of the 42nd New York Film Festival (“Tropical Malady” being the other). But if you ask the guy who sat in front of me during the press screening – well, you’d have to wake him up first.

The world breaks down into Godardists and non-Godardists the way it breaks down into Democrats and Republicans, smokers and nonsmokers, cat people and dog people; there’s a bit of slippage between camps, but not much. When he stopped making genre movies about the inability to make genre movies, many people renounced their affiliation. The unclassifiable late work has exacerbated this division. Exquisite esoterica like “Nouvelle Vague” or “In Praise of Love” place insurmountable demands on even the most sympathetic cinephile.

So while “Notre Musique” is being hailed as the kindest, gentlest, least obscure of the late work, keep in mind that even at his most lucid, JLG is never ABC. At Cannes, where the name of the game is to cover as much ground as possible, most everyone who liked the film saw it twice, even three times – because they had to. Mr. Godard works hard; his films are hard work.

Mr. Godard has famously said that movies need a beginning, middle, and end – but not necessarily in that order. “Notre Musique” is divided into Hell, Purgatory, and Heaven – in that order. Hell is an astonishing 10-minute montage of war imagery, part documentary, part fiction. We are confronted with an unrelenting display of terrible things, given terrible beauty by a virtuoso handling of the video texture. The director of “Les Carabiniers” is setting his first theme into motion. War (politics) and the representation of war (art) share the exact same source: the imagination of man, with all its primitive dictates and will to transform.

An hour of Purgatory is staged in Sarajevo, where Mr. Godard has been invited to lecture on “The Text and the Image.” An Israeli journalist (Sarah Adler) interviews a Spanish novelist in “a place where reconciliation is possible.” In the lobby of a Holiday Inn, a Palestinian poet muses on the victory of the vanquished. Godard’s extraordinary lecture uses the shot/counter shot structure of narrative filmmaking as an all-purpose metaphor to reflect on everything from the Middle East, to the American civil war, to the inability of Howard Hawks to distinguish between a man and a woman – this last bit giving us one of the great cockeyed moments in all Godard. At the end of the lecture, someone asks whether the new digital cameras can save the cinema. The oracle remains silent.

In Purgatory, modes of neorealism jostle pure formalism, documentary blurs with fiction, quotation tangos with dialogue, and Native Americans out of central casting materialize in the ruins of the Sarajevo Public Library. The harmony of “Notre Musique” rests in the freeing up of voices; Mr. Godard has relaxed his vice-grip on the bookshelf. As ever, his formal inventiveness is staggering. His particular way of arranging material into avid, asymmetric structures is closer to Thelonious Monk or Paul Celan than to anything in the cinema.

It’s heavenly even before we get to Heaven, a lakefront pastoral guarded, with heart wrenching poignancy (and no small irony), by American soldiers. As a strain of transcendentalism has crept into his pictures, Mr. Godard has shown us fleeting views of paradise here and there, but this extended sojourn feels hard-earned, clear-eyed, wrestled with great effort away from the darkness. The cannibal jungle from “Weekend” has been redeemed; the mimes of Antonioni’s “Blow Up” have gone on holiday.

That Mr. Godard sees everything through the lens of cinema will always drive people bonkers. Cinema is far from dead, but his generation’s faith in its transformative, utopian capacities died a long time ago. Still, he persist and resists, and in his twilight years has quietly begun to sing: “The Principle of Cinema: Go towards the light and shine it on our night. Our music.”

– Nathan Lee

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Sarah Adler, the heart of “Notre Musique,” brings – like actresses Anna Karina, Anne Wiazemsky, Juliet Berto, and Myriem Roussel before her – exquisite grace and life to Jean-Luc Godard’s dense, distant, difficult work.

Born in Paris, Ms. Adler, 26, lived in Israel from the age of 10 until 16, then moved to New York to attend theater school. She has spent the last few years shuttling between the City of Lights and Tel Aviv, with the occasional stop in Gotham. “I’m completely Israeli – as well as French and a New Yorker,” Ms. Adler says of her plural identity.

Was she at all nervous about meeting le seigneur du cinema? “Sure, I was a little nervous. He’s a person who has this aura around him, but I really wanted to see this man, and not be blinded by the legend part.”

Although Mr. Godard, Ms. Adler says, “can be very specific and really knows what he wants,” she believes he also gave her freedom with her character, the impassioned, righteous journalist from Haaretz who attends a literary conference in Sarajevo. “In a way I think what he wanted was for me to be as me as I could. I think he liked the fact that I have this plural identity and don’t belong to one place.”

Still it was the differences between her character and herself that in part concerned her. “Of course you do have to ask yourself, ‘Am I doing a character that I agree with? What am I saying here?’ It’s a very delicate subject, and for me being Israeli, I was concerned.”

The importance of ‘Notre Musique,’ Ms. Adler says, is not the statements it makes but the question it raises. “What’s generous about ‘Notre Musique’ is that it looks at this pain, it has this strong questioning of why is this happening again, why are human beings constantly in war, this never-satisfied need to kill each other and to have power over the other. It’s not optimistic, but this is hope – to still question so strongly is a hope.”

Early in our conversation, Ms. Adler has lit up at a table outside on Broadway and 64th Street, graciously enduring the antismoking harangue of an indignant middle-aged man. Later a homeless woman asked the actress if she had a cigarette, which she politely proffered. Noticing the exotic packaging, the woman wanted to know the cigarette’s provenance; when told the pack was from Israel, she declined the gift and huffed off.

“See? The world is going crazy,” Ms. Adler, astonished, said.

– Melissa Anderson