An innocent immigrant woman (Marion Cotillard) is tricked by a man (Joaquin Phoenix) into a life of burlesque and vaudeville until a dazzling magician (Jeremy Renner) tries to save her and reunite her with her sister who is being held in the confines of Ellis Island.

Cotillard carries cabaret from hell.

The Immigrant could have been called 'Out of the Frying Pan and Into the Fire’. The frying pan would be Poland after the First World War and the fire would be New York City, circa January 1921.

Cotillard is at one with her role

Sisters Ewa (Marion Cotillard) and Magda Cybulski have sailed to America in search of that thing the United States is supposed to specialise in: A better life. But upon arrival, Magda is suspected of having an illness the USA has no interest in importing to the mainland. She will be quarantined in the infirmary on Ellis Island for six months. "If she doesn't get better, she'll be deported," says an immigration official.

Magda may well be ill and she may have to turn around and go back without getting any closer to the REM sleep portion of the American Dream, but her sister faces an even thornier dilemma. Ewa is told "You may be a woman of low morals. Is that true?" We in the audience can tell that Ewa is upright, compassionate and honest but for some reason the immigration official can't see what we see. "We do not allow unaccompanied women into this country," says he.

Back in Poland, Ewa worked as a nurse to a diplomat and so speaks some English. Just enough, it turns out, to mistake ulterior motives for a sincere offer to help.

With the collusion of certain staffers, Bruno Weiss (Joaquin Phoenix, in his fourth collaboration with James Gray) uses Ellis Island as a sort of virtual casting couch. He is a low level impresario, scouting talent for a seedy cabaret. The women he hires and houses do appear on the stage but that's just a façade. To be a female in Bruno's clutches is to be forced into the world's oldest profession.

Ewa manages to find her aunt and uncle but the reunion goes badly because the uncle has heard that his niece indulged in unvirtuous behaviour on the boat. Once you're a "fallen woman" (perceived or genuine) it's almost impossible to get back up.

Ewa's goal is to remain alive and save some money so that she and Magda can be reunited. Given her current occupation, Ewa's self esteem isn't anywhere near as elevated as the torch she holds aloft in her painfully ironic costume as the Statue of Liberty during each day's show. The laser hasn't been invented yet, but in Ewa's sordid surroundings you could say her focus resembles what that device is known for. We tend to think of physical attractiveness as a plus in life but, to a certain extent, Ewa is singled out for exploitation because she's pretty.

Orlando the Magician (Jeremy Renner) comes to perform. He has boyish energy to burn. He and Ewa fall for each other. After the film has been running for 90 minutes (and every woman in the audience, pretty or not, is thanking her lucky stars that she wasn't an immigrant in 1921), they kiss. But Bruno is horribly jealous.

However one responds to the film in its entirety, Cotillard is at one with her role. We can put ourselves in her uncomfortable shoes and wonder, "What would I do in her situation?"

A colleague who was on the set said it was difficult to see what Cotillard was "doing" in person but projected huge on the big screen, her moves were those of a silent movie actress. Still, Ewa is called upon to speak.

"There were 20 pages of dialogue in Polish and only 2 words sounded similar to French or English," Cotillard explained at Cannes.

A Poland-born colleague confirmed that Cotillard's memorised-by-rote Polish dialogue is remarkably good. "Not perfect, but as close to perfect as a non-native might be expected to achieve."

But what Cotillard achieves goes beyond skilful linguistic mimicry. When we observe Bruno's actions, we think "Hmm, there's Joaquin Phoenix playing a tortured soul and going a bit overboard, although he's really got raw material to be tortured about." When we see Orlando (that's his stage name), we think "This is a kind of role I haven't seen Jeremy Renner play before and he's quite energetic and appealing." But whenever Cotillard is on screen, we think "There's Ewa – I sure hope she makes it."

In Gray's period New York, there's a sense that something emotionally unpleasant or unethical is going on behind every other door.

"Kubrick said he always wished movies would be more daring and more sincere," says Gray, whose original title for his semi-daring and deeply sincere film was 'Lowlife’ with a detour by 'The Nightingale’ ("Everybody hated that title!")

The Immigrant is a fine title. If you are reading this, whatever your continent, there's a good chance your ancestors hailed from somewhere other than where you happen to be right now. Wave after wave of people left their original homes between 1900 and 1924 to sail to New York. "Forty percent of Americans can trace a relative who was processed through Ellis Island," says Gray. That includes him.

"I guess I'm unabashedly pro-immigration," says Gray, whose Russian relatives made the journey in the period depicted.

Ewa is 'American’ in that her virtue has been compromised but nothing can dent the resolve she manages to maintain. Although her daily reality happens to be renting her body out for money – little of which accrues to her – she thinks of this as temporary, just as her sister's quarantine is temporary. Both conditions involve what they brought with them – their bodies – and in Ewa's view, both can be "cured". In America, you can reinvent yourself and start over – more than once if necessary.

In addition to its exploration of faith and possible redemption, The Immigrant contains a strong subtext about showbiz and entertainment, as well as commerce, American-style. Forcing women into prostitution is "just business" and "nothing personal". Bruno yearns for Ewa. The feeling is not mutual. But the show must go on!

Every girl at the secret brothel has an assigned stage persona. Ewa is cast as Lady Liberty, her costume a cheap but unmistakeable approximation of the statue France gave to America, the sight of which means "Your boat has made it to America, now it's up to you to make it in America."

That shorthand is so universally understood that one is tempted to ask, "Uh, what would we have done if Bartholdi hadn’t sculpted this particular female and sent her on her way? (Readers who can't get enough of symbolism will note that the Statue of Liberty is in the form of a woman moulded by men to their specifications.)

Although the story doesn't always cohere or convince as much as one might wish, Gray and his production team have taken great pains to get the historical details right. One surprising – and true – passage shows the great Italian tenor Enrico Caruso performing for those detained on Ellis Island. In Apocalypse Now Redux, Francis Ford Coppola touches on how incredibly odd it was to import rot-gut American entertainment for the troops stationed in the hot, damp terrain of Vietnam. Here, the entertainers have a shorter, safer commute, but the effect is equally surreal.

Just about everybody in The Immigrant may have misplaced their copy of the Declaration of Human Rights, but a perfectly sung operatic note needs no administrative documents to work its magic. Art, like people, was meant to cross borders.