I stand up to greet Timothée Chalamet and he shakes my hand. “Nice to see you again,” he says. Endearingly, he thinks we’ve already met — sadly, we haven’t, although his face is awfully familiar. The posters for his new Netflix film are everywhere, proclaiming “All Hail the King.” I’m not sure if they mean King Henry V, the character he’s playing in a film adapted from Shakespeare’s history plays, or Chalamet himself who, at the tender age of 23, is fast becoming Hollywood royalty. And I’ve seen the pin-up du jour draped across magazine spreads and on Instagram — both his official account and the @chalametinart account that photoshops his face on to classic works of art (my favourites are The Lute Player by Caravaggio and the timely Head of Prince Hal by Charles Robert Leslie).

We meet one scorching afternoon the day after the premiere of The King on a private island in the Venice lagoon. Chalamet is tall, far taller than I expected; a pale thin duke just shy of 6ft. He’s wearing a navy-blue loose-knit sweater and sunglasses and, in a feat of co-ordination, balances an espresso cup and saucer in one hand as we shake with his other.

The posters for his new Netflix film are everywhere, proclaiming “All Hail the King.”

The night before he had greeted crowds of fans on the red carpet at the Venice Film Festival wearing a double-belted silver suit by the designer Haider Ackermann with a dandyish silky blouse underneath. It’s the kind of adventurous choice that has turned Chalamet into a style icon — and one of the main draws on the Lido.

His hot reception in Venice rivalled that of older, more established stars such as Brad Pitt and Johnny Depp (the latter the father of Chalamet’s girlfriend, more of which later). Those guys looked like old news compared with Chalamet. When one fan burst into tears, he gave him a generous hug, while his security stood by nervously. Chalamet is no longer the next big thing — he is a big thing.

His hot reception in Venice rivalled that of older, more established stars such as Brad Pitt and Johnny Depp.

But is he any good? As with all royalty a question lingers: does he deserve it? Is this merit or luck? At the press conference for the film he is careful to stress how much he’s still learning. Here with me, he’s courteous and charming, and when answering questions, he fixes me with a stare, talking quickly, sometimes letting his words get away from him, folding and unfolding his long body, rubbing his hands and gesturing fluently. His familiar abundant locks have grown back, though for much of The King he sports a brutal bowl cut. It’s the male equivalent of the unforgiving Joan of Arc look.

He laughs when I ask him about the medieval hairdon’t. “I think it was hugely important because that’s what was true to the period,” he says seriously, before asking: “Are you going to get one? Are you going to get a bowl cut?” Absolutely not, I say. Then again, if anyone’s going to make bowl cuts trendy, it’s going to be Chalamet — that’s winter 2019 sorted.

Chalamet grew up in Hell’s Kitchen in Manhattan; his father, Marc, originally from Nîmes in France, is an editor at Unicef, and his mother, Nicole Flender, a New Yorker of Russian and Austrian Jewish descent, is an estate agent and former dancer. There are showbusiness folk on her side of the family (Chalamet’s maternal grandfather was a screenwriter and his uncle a director) and Chalamet attended Al Pacino’s former school, LaGuardia High School of Music & Performing Arts in Manhattan, the inspiration for Fame. Fellow students included Lourdes Ciccone, Madonna’s daughter, whom Chalamet dated for several years; another classmate was Ansel Elgort (Baby Driver and The Goldfinch).

Fellow students included Lourdes Ciccone, Madonna’s daughter, whom Chalamet dated for several years.

While there, Chalamet lost out on a couple of big parts to Elgort and on the title role in Spider-Man: Homecoming to the British actor Tom Holland (he has described his “total panic” in the audition). He did, however, have a memorable role in the TV series Homeland as the president’s off-the-rails son, and was cast as Matthew McConaughey’s son in Christopher Nolan’s Interstellar. His time at LaGuardia inspired what many fans consider his greatest moment: the “Timmy Tim” video in which he raps a eulogy to his high school statistics teacher. It has notched up more than 2.3 million views on YouTube.

Laurence Olivier in Henry V, 1944.

It was the role of Elio in Luca Guadagnino’s Call Me by Your Name in 2017 through which Chalamet entered public consciousness. He played a teenager falling in love for the first time one long hot Italian summer. It was a role of intimacy and poignancy, and included a notorious scene with a peach that Chalamet has previously referred to as “the most awkward scene to see with your parents in the whole world”.

The film won him a passionate teenage fanbase and industry recognition. He became the third youngest actor to receive a best actor nomination at the Academy awards and his bromance with co-star Armie Hammer played out over social media. The same year Chalamet proved he could do comedy in Greta Gerwig’s Lady Bird, as Saoirse Ronan’s crush, Kyle, a poseur extraordinaire. Gerwig described him as “a young Christian Bale crossed with a young Daniel Day-Lewis with a sprinkle of young Leonardo DiCaprio”. Try living up to that.

“The most awkward scene to see with your parents in the whole world.”

Since then he has been Steve Carell’s drug-addicted son in Beautiful Boy, a role for which he auditioned six times; he has co-starred with Christian Bale in Hostiles and played Gatsby Welles in Woody Allen’s A Rainy Day in New York. The Allen movie thrust him into the middle of the Me Too controversy and, after an outcry about his participation in the film, Chalamet donated his salary to various charities, writing in an Instagram post: “I am learning that a good role isn’t the only criteria for accepting a job.” I am told that Chalamet hasn’t seen the film.

The King constitutes another step up. Chalamet plays Henry V, a rite-of-passage role previously performed by Laurence Olivier, Kenneth Branagh and Jude Law. Will audiences accept this New Yorker with a French passport as the victor of Agincourt? Prince Hal and Chalamet — who has Hal for a middle name — are both asking: am I good enough to play the King? From beautiful boy to grown man: can he pull it off?

It seems so. His performance has led Variety to conclude that Chalamet “could be the biggest movie star of his generation”. His co-stars are effusive in their praise. Ben Mendelsohn, who plays his father Henry IV and is not prone to luvviness, tells me: “He’s a f***ing fantastic movie star. He may be a better movie star than we deserve. I mean that quite seriously. He’s something of a gift.”

Will audiences accept this New Yorker with a French passport as the victor of Agincourt?

I ask the film’s director, David Michôd, why he cast Chalamet. “He’s a true boy king. I wanted to take that beautiful soulful foppish kid from Call Me by Your Name and turn him into something hardened,” he says.

Chalamet’s Henry is not the epitome of English heroism. His rise to power is something darker. It’s a challenging transformation and I wonder if the film was shot sequentially. Chalamet explains: “It’s rare on movies to get the good fortune of shooting chronologically. On Call Me by Your Name we did. [With The King] David was super-precise about what he wanted. We had a lot of conversations before the movie about when, if ever, there would be a moment where Hal — I don’t even know what the word would be — thinks he metastasises into a leader.”

Chalamet is careful when I ask him whether he would like Henry V if he were to meet him: “What a young man would have aspired to, and the language of courage and the border-expanding, that would be … jingoistic,” he says. “It’s really not how people, and especially young people like myself, talk about the world today, or feel about it. My point of view, it doesn’t match up with the period.”

For Chalamet the appeal of the character is the “struggle in [his] ascendancy or the stress [of it] … to go through that at a young age”. He’s less interested in “the honour of it, or the goodness in it”, he says.

As well as proving his acting chops, Chalamet has to do some serious fighting. “I did put on 15lb for the movie,” he says (don’t expect a Christian Bale-style transformation, but he does look slightly more filled out). “But this wasn’t the warrior version. I think for the fights, it’s less that Hal goes in there like Troy or Gladiator or something. Hal’s less kicking ass and more just surviving. The valiance comes more from just showing up without a personal guard the way the Dauphin [played by Robert Pattinson] does.”

“It’s really not how people, and especially young people like myself, talk about the world today.”

He smarts at some critics who, rather snippily, have compared the Battle of Agincourt scene to the “Battle of the Bastards” in Game of Thrones.

“Now they say that shot looks like the one from Game of Thrones, but that episode hadn’t come out when we were making it. It’s not like there are only two directors to have used a crane shot,” he says, defensively.

We talk about the end of the film and, though concerned about spoilers (“Use your discretion,” he says, seemingly forgetting that a version of this story has already been told by one William Shakespeare), he does say that he feels Henry “has taken a step in the right direction and finally found someone who is a guiding light. An honest light.” That person is the French Princess Catherine, played by Lily-Rose Depp — daughter of Vanessa Paradis and Johnny Depp — with whom Chalamet is romantically involved. Both half-French, half-American, they met on set. After our interview, images of them kissing on a yacht in Capri go viral. This week American papers reported that they were “smitten” on a date night in New York.

At Christmas we will see Chalamet reunited with Ronan in Gerwig’s star-studded adaptation of Little Women. Chalamet plays Laurie, the March sisters’ next-door neighbour and the great friend of the book’s heroine, Jo March — until he declares his (tragically unrequited) love for her. “With Greta I just feel that I’m so in step with her when we work,” says Chalamet, who is clearly at home in period drama. “Well, almost everything I’ve done is a period piece,” he says. “Call Me by Your Name is Eighties …” He is also showing signs of an interest in getting behind the camera. “I wasn’t the lead in [Little Women] so I felt like, ‘How can I help?’”

Chalamet plays the lead in Denis Villeneuve’s big-budget remake of Frank Herbert’s sci-fi epic Dune, released next year; there’s a role coming up in the new Wes Anderson movie The French Dispatch and a rumoured follow-up to Call Me by Your Name, entitled Find Me. André Aciman, the author of Call Me by Your Name, will publish his sequel this month. It will check in with Elio, now a classical pianist living in Rome, and Oliver, now a New England college professor with a family, and explore what has happened to Elio’s father, Samuel.

It’s time for me to leave. “Good to see you again,” Chalamet says, with the good manners of a Golden Age star, as we get up. I ought to correct him — we really haven’t met before today — but who am I to contradict the King?