Leviathan: the Cannes hit which absolutely definitely doesn't put the boot in to Putin

To look a bit upset when someone else wins a prize is understandable. To look upset when you've won, less so. But such was the case early on at the Cannes closing ceremony last Saturday, when Andrey Zvyagintsev's Leviathan was named best screenplay.

Why? At Cannes, a film can win just one award. Best screenplay meant Leviathan wouldn't hook a bigger fish – in particular, the Palme d'Or.

In fact, Zvyagintsev held his composure better than many who'd tipped it for victory. Just a flicker of disappointment – or confusion – creased his face as he strolled down to collect his ceremonial scroll. The curses came from those who'd negotiated the big US distribution deal, journalists now deleting their pre-cooked news stories. From punters who'd had a flutter following the film's rapturous reception, and editors scrambling to rethink plans about what the win might say about resistance to Putin.

For Leviathan is not just a masterpiece; it's a polemic against the current Kremlin administration. Its appeal is not just its brilliance, but its ballsiness. One scene shows friends taking literal potshots at framed photos of former Russian presidents. Putin's portrait hangs above the desk of the corrupt local mayor, who's forcing our hero from his family home so he can build his own palace on the site. A priest speaks of "reawakening the soul of the Russian people", as their spirits lie crushed at his feet. Corruption is so endemic, these people have even lost God.

You meet Zvyagintsev, then, expecting a firebrand. You find a discreet diplomat, bright white shirt, snazzy blue wool tie, eyes kind behind designer specs. He sits neatly next to the translator, smart little pouch containing phone and wallet, zipped tightly by his side. "My goal," he says, "was certainly not to confront power. Particularly considering that the film got financial support from state bodies."

It's true, this does complicate the picture – 35% of the budget was stumped up by the Ministry of Culture. The minister himself saw the film a couple of days ago. "He said it was good but he didn't like it. I can understand that – he has a lot of other work to do. He is supposed to make the world better. What we are doing is creating a work of art. Art must provide light – it should give people hope."

At the press conference, then again on the beach the next day, Zvyagintsev proves unshakably moderate. He does not ruffle and he will not be pushed, which is as much down to his own personality as the two mute flunkies who listen in on the interviews. "The minister obviously has a firm stance," he continues, "and that cannot but be respected. Two days ago, when I spoke with him, I said I had two projects I hoped would take shape. He said: "'Well, show me the screenplay!'"

Zvyagintsev's producer, Aleksandr Rodnyanskiy, expresses more scepticism about the potential damage to future working relations. "The minister gave a quote to Le Monde," he said. "'All flowers can grow, but we only water the ones we like.'"

And there is a flashpoint looming: the introduction in Russia on 1 July of new legislation outlawing swearing in the cinema. Zvyagintsev selects his words slowly, as if from an expensive shelf: "If it is implemented, we should still be entitled to screen as we shot beforehand," he says. "And I don't think we used too many swearwords; each was weighed up very carefully."

What about the general wisdom of such legislation? A further pause. "These laws that ban things aren't very suitable, in my eyes," he says. "I do indeed hope that we will reach mutual understanding, that freedom will prevail. I think in all countries around the world, the problem of liberty is important; it's the duty of everyone to combat the state and uphold liberty – to address it in an honest, frank, forthright manner."

This leads him to the other reason that Leviathan isn't, despite all appearances, an attack on Putin: it was inspired by a case in Colorado. In 2004, Marvin Heemeyer, a 52-year-old welder and the victim of expropriation, drove a bulletproof tank into town and demolished a dozen municipal buildings before shooting himself. Initially Zvyagintsev wanted to shoot his story – which borrows the spur, rather than the plot – in America. "But time went by, the project evolved and I thought it better to set it in Russia." He sips a little water. "Stories like that amaze me. You would never think that in a democratic country something like that could happen. It's the story of someone in despair. No one was listening. No one was taking account of what he was saying."

Zvyagintsev knows what it is to not have a voice. Now 50, he served in the army for two years after high school, then studied acting at university. But for a decade, offers of work failed to flood in. He worked as street cleaner and an extra, much of the time so impoverished he struggled to buy bus tickets. Then, at the turn of the century, he caught a lucky break directing TV, primarily soaps and cop shows. He proved so good so fast, he easily rustled funds to make The Return, a brooding family drama which came from nowhere to take the top prize at the Venice film festival in 2003. The Banishment (2007) and Elena (2011) followed.

Leviathan is his most accessible to date, in part because of the humour in its bloodstream, and much of that on account of its high alcohol content. His characters' idea of a birthday party is to head to a deserted lake with their wives and children, get absolutely wasted, then get out the guns. Right through the film, they stagger round, cautioning each other not to drink so much. "Are you all right to drive?" one woman slurs at her husband, as he lurches, paralytic, towards the front door. "Of course," he replies. "I'm a traffic cop."

No, says Zvyagintsev, there was no exaggeration for comic effect – though he's pleased that people found it funny. "When the Greeks drank wine, they would add water so it wasn't so strong," he says. "When something is tragic, you add comedy." He tells of a game in Russia that seems to solely involve downing a half-litre bottle of vodka in one. But Russian people don't drink as much as the Finns, he protests, who flood into St Petersburg every weekend on account of the cheaper booze. "Even here! Last night, after we made sound checks for the screening, we came out at 3am, and there were three ladies walking along so drunk. It's the same everywhere."

So: Leviathan, once and for all, isn't about Russia. Its themes are universal, its conundrums eternal. Even what it says about patriotism, and the way it can be channelled by authority figures for ill ends and land grabs, is applicable the world over. "Patriotism is to me an instinct. You need to belong. Your life must have a meaning. And it's very easy to use that feeling."

But then, just as I'm going, a flash of fire behind the glasses. "The dream for my country is to have fair laws. So the people would be able to foresee a certain future and believe in it with perspective. Which is not the way it is now." He smiles mildly again, and straightens his tie.