You know who Oscar Isaac is. But you may not know you know. He played Carey Mulligan's husband in Nicolas Winding Refn's Drive. He played Abbie Cornish's fling in the framing sequence of Madonna's ill-starred W.E. Now 33, handsome in the old-school matinee-idol style, Isaac has been plugging away since he left the Julliard School in 2005. But all his ships have finally come in with the release of the Coen brothers' funny, sad Inside Llewyn Davis.

Early adopters of the Isaac brand could be forgiven for not immediately recognising their hero on the film's posters. Roughed up in a corduroy jacket, his hair an unruly squabble of curls, he is depicted strolling morosely down New York's MacDougal Street with an uninterested ginger cat in his arms. His character modelled on nearly-man Dave Van Ronk, Isaac plays a talented folk singer who seems doomed to miss out on the acoustic boom that is about to hit Greenwich Village in the early 1960s. Apparently, T-Bone Burnett, the unstoppable musicologist who provides the film's authentic sounds, tipped off Joel and Ethan Coen to the rising star's potential.

“They had told the story to T-Bone and he told him to look at this guy,” Isaac remembers. “T-Bone said: ‘He’s a good actor, he’s a good musician and he’s not a square’.”

Praise indeed. Does he see himself in that description?

“I think so. I was a bit of a musical whore when I was younger. I was in all these punk bands. I was in all these ska bands. I can see that.”

Llewyn Davis’s ethnic origins are playfully muddled. Oscar’s surname points towards the Jewish influence (think of one Mr Robert Zimmerman) that was much afoot in the early folk scene. But the character’s name suggests Welsh origins. Dave Van Ronk, a respected journeyman to his death in 2002, had Swedish ancestors. But Oscar Isaac – born Oscar Isaac Hernández – is of Guatemalan and Cuban descent. It looks as if he had a very respectable upbringing. Dad was a respected doctor. He was raised in a middle-class corner of Miami and ended up at one of New York’s most respected drama schools.

“My dad was a frustrated artist,” he muses. “He made little movies with his brother. So, they have always been very supportive.”

Inside Llewyn Davis depicts a world that (though it's not aware of the fact) is waiting for the arrival of Bob Dylan and the re-invention of popular culture. Davis is greatly respected by the cognoscenti, but nobody seems very interested in handing him any serious money. As was Dave Van Ronk, the protagonist is a sort of John the Baptist figure. He is laying the groundwork for a coming messiah.

“Exactly. This is right before that all happened. The old is dying and the new hasn’t quite been born yet. He’s paving the way. His head will be on a silver platter. Ha ha!”

At one point in the movie, Davis brandishes an album that is mocked up in exact imitation of Van Ronk’s first record. The Coens are not making any secret of their inspirations here.

“He’s still a fresh creation – as much as any character can be,” Isaac muses. “But there is a lot of Van Ronk in the character: his repertoire, his surliness, his origins as a kid from the New York boroughs, his time as a merchant marine. The fact that he is blue-collar guy -- not someone trying to reinvent himself. All that is from Van Ronk.”

Inside Llewyn Davis has its wistful qualities. Filmed in a lovely haze, the picture goes among singers slyly modelled on the Clancy brothers and Peter Paul and Mary. The middle section of the film finds Davis going on a sort of odyssey from New York to snowy Chicago, where – this being a Coens film – he doesn't really pass through any epiphanies.

Music historians still argue as to how a few musicians in a few coffee shops went on to transform popular culture. Davis is keen to stress the influence of the legendary musicologist Alan Lomax, whose field recordings brought the folk songs and spirituals of remoter corners to an urban audience.

“I don’t know quite what it is about that time,” he says. “But it did have to do with a connection to American roots music. When Lomax came down and made all these field recordings and broadcast these songs of desperation across the globe, that was the single most democratising act in the history of music. That need to reconnect was a very important thing.”

Inside Llewyn Davis may summon up smoky nostalgia for an era most viewers will only have experienced second-hand, but the piece still throbs with the Coens' characteristic cynicism and pessimism. The film does, after all, focus on a grumpy fellow who is destined for relative obscurity. There is sort of grim resignation about the character. He would, one suspects, be astonished if his record managed to become a hit.

“He sees himself as a guy who is never going to make it,” Isaac agrees. “There’s a great Van Ronk quote: ‘Would I like to have made a little more money? Sure. But I did end up doing what I wanted to do. Even when I wanted to get out, I was pulled back to the music’. If he could have he would have.”

Isaac must understand that. Nobody goes into acting for the money. A few child stars aside, every performer has to fight against rejection.

“Yeah, I am a little bit of a determinist, that way,” he says. “I don’t know if free will really exists. The choices you made are the only ones you could have made. I do think that. I became interested in what I am doing at an early age. I was able to work on the skills since then. That makes it seem predetermined.”

Since the film premiered at Cannes way back in May 2013, the word has gone out that Isaac is playing some sort of prime jerk. He is certainly a sponger. His sometime girlfriend (Ms C Mulligan again) – revealed to be pregnant early on – can only speak to him in hisses and curses. He is disobliging to his decent blue-collar family. But Oscar doesn’t enjoy hearing his creation being dissed. After all, when he accidentally allows his uptown friend’s cat to escape, he tracks him down and, locked out from the apartment, lugs the beast around a snowy city.

“People have said all that about him,” he says. “But that’s not really true. He’s just straightforward about things. He’s not all that selfish. He spends almost the whole movie trying to take care of this fucking cat. A lesser person would have said: ‘These things happen.’”

He has a point. Davis’s problem (if it is a problem) is that he makes no effort to empathise or compromise. He just says what he means and becomes confused when offense is caused. Dylan may not have been an easygoing guy, but he was prepared to tweak his persona. Davis is what he is. He is not at home to charm. He’s not at home to reinvention.

“That’s a rare thing,” Oscar says. “I wondered if I could convey warmth without the usual means. He’s a guy who never says: ‘I mean you no harm’. I loved experimenting with that. I went to parties and did that. It was really scary. You tell a joke. But you don’t let them know it’s a joke. If they get it, they laugh. If they don’t, they think you’re an asshole and move away.”

You sense that Davis is not just acting. He is creating and inhabiting a character. Davis’s aberrations appear in the script. But Isaac has added flesh, blood and sinew to the skeleton.

“For me, I can never tell how a film is going with an audience,” he says. “But I saw it with a couple of buddies and that was heavy. When we left, we were talking about it. And I knew it was a good sign when they referred to the character as ‘him’ and not ‘you’. They hadn’t even noticed they were doing that.”

The Coens' methodologies remain elusive. Now deep into an awesome run of form with films such as A Serious Man, True Grit and No Country for Old Men, the brothers are as lauded as ever. But they don't come across as particularly verbal people in interviews. Whereas we have hours of Martin Scorsese explaining himself, Joel and Ethan communicate through enigma and evasion. Is it any different on set?

“No, not so much. Or they don’t verbalise the things you think they might verbalise,” Davis says. “They don’t go for the big ideas or ‘meaning’. They are practical and pragmatic. It’s to do with an adjustment of pace or inflection here. Make the line mean this or that. Joel distilled directing down to ‘tone management’. I was taken aback by that.”

One imagines they had little luck trying to manage the poor old cat’s tone. The various animals who play Ulysses (its owners are highbrow folk) deserve some sort of massed recognition during the current awards season. Sometimes he’s restless. Sometimes he’s relaxed. How the heck do you set about training a cat? It has been said that the only way to get a cat to do something is to persuade said animal that it was his or her idea all along. Apparently, this describes the process quite accurately.

“They have four of five different cats with very different personalities,” he explains. “The one on the poster is the more sedate one. Then they have one that squirms more when they need it to move and jump. Often they were tied to me, so they wouldn’t run into traffic. It wasn’t so bad. But they can’t really be trained.”

Does he get on with cats?

“No. Not really. Sometime ago I had to go into hospital when a cat bit me and it infected my lymphatic system. So, no.”

By the end of the experiences did he like cats any more or any less?

He pauses.

“Hmm? No. About the same, I’d say.”

Llewyn might not have been so diplomatic.

yyy Inside Llewyn Davis opens next week