What a pretentious wanker I am!" shouts Sting loudly. We are on the French Riviera, sitting at a quiet table on the balcony of the house – now a hotel – where F Scott Fitzgerald wrote Tender is the Night, and I have just reminded Sting of a remark he made in 1987. Then a 36-year-old superstar promoting a new album, Nothing Like the Sun, he declared: "I don't want to be a pop star all my life. I'd quite like to be a balding, rotund, Jungian analyst between 40 and 50."

Twenty-six years on and he is anything but. He cringes and claps his hand over his eyes. Now 61, he is still a superstar, back on the promotional rollercoaster after some years away. In slim black jeans, motorcycle boots and a T-shirt darkened with sweat from the soundcheck he has just come from, he is anything but rotund – in fact he is lean and sinewy. And he is pretty far from bald – even if his close-cropped silver and blond hair provides only light cover in places.

"So, here I am," he says. "Still doing that job – but I'm happy. And anyway," he pauses and looks out over the azure water below us, "I don't think I'd get anything like as much money as a Jungian analyst."

That night I go to watch Sting performing in a large amphitheatre just off the beach in Juan-les-Pins. Around 3,000 people are seated in rows banked up from the edge of the sand and away from the sea. When I make my way down row C, I find myself sitting next to Julian Lennon, who has driven over from his new place in Monaco. The show is slick, supremely well-rehearsed and overflowing with hits – as far as you could possibly get from punk rock, and that is sort of the point. It is also the reason Sting has been so roundly vilified – at least by the UK press. He does precisely what he wants, in the way he wants to do it.

"In my band everybody knows their job," he tells me later. "Nobody's fighting for my position, so it's very stable. Creative instability shouldn't be in the politics of a band. That's tiresome. I've done all that."

As he stares down the barrel of his seventh decade, Sting is at a distinct remove from Macca or Elton or Weller or Jagger – he is not intent on the idea of staying in the game.

"Elton's a real pop guy," he says. "He loves it. He buys all the records; it's his lifeblood. But that's not me, I want to be a grownup." For Sting, surprise is everything. Which is why his new record, The Last Ship, is a song-cycle built on memories of his childhood growing up in the shadow of the Swan Hunter shipyard in Wallsend on the banks of the River Tyne. He wrote the songs for a musical of the same name, which opens on Broadway next year. This is not a man with a shrinking sense of ambition.

"I'm given the licence to do things by previous successes," he says. "Those successes meant I could walk into my record company and say: 'I'm making a record of 16th-century art songs on a lute,' and they say, 'Yes, Sting.'"

Have they ever rolled their eyes and said: "Obviously, we like that idea but, er, could we have a Christmas album too?"

"No," he laughs, as if the very idea is ridiculous. "They understand my kind of madness.

The Police: Sting with Stewart Copeland and Andy Summers in 1975. Photograph: Barry Schultz/Sunshine/Rex Features

In 1986 Sting said getting the Police back together would be "a step into immaturity and regression", but in 2007 they reformed for a world tour and sold 2.5m tickets in days. "We made a shitload of money," he grins. "The timing was perfect and I take full credit for that. It was an exercise in nostalgia. We were realising an asset, for probably the last time."

In 1978, when their manager, Miles Copeland, first secured them a deal – with no advance, meaning no "feudal relationship" with a label – the Police were so poor that they stole a master tape belonging to the band Renaissance from the studio they were in and recorded over it. "It was criminal," Sting admits, "but we didn't have a choice: we simply couldn't afford two-inch tape. Can I still be prosecuted for that, do you think?"

The poverty didn't last long. In 1981 they sold 10m records in 12 months, more than the Rolling Stones had sold in the previous 18 years, and Sting never stopped selling records in eye-watering numbers. Ultimately, there came a point where he felt he owed a debt to his old bandmates, Andy Summers and Stewart Copeland. "There was a certain amount of guilt," he says. "The Police were a vehicle for my songs. I believe that very strongly, so I needed to look after them to an extent. Not that they were begging, they're too proud to do that. But they were very happy to do the tour."

So it was a good payday for them?

"It was a fucking great payday for them," he says.

The two words people still think of when they think of Sting were uttered by him more than 20 years ago. Yet when I mention tantric sex, rather than looking annoyed, he beams with pleasure. "Bob [Geldof] and I were pissed when we did that interview [with Q magazine]," he says. "I was just trying to wind him up. That quote went round the world like wildfire, and it's still going round."

Did he enjoy how much it annoyed some people? Like, here was this zillionaire, yogic high-flyer rubbing our faces in it again ...

"Of course," he says. "For a while I would say, well, five hours of sex includes a movie, and that worked for a while, but at the same time, I do believe sex is the most important thing that we do with someone we love: it's a spiritual expression. It's not just a Friday night bunk-up."

Not that there's anything wrong with a Friday night bunk up …

"No, but it can be a beautiful, extended sacrament too."

I ask Sting if he thinks he has been fairly treated by the press and he laughs even louder. "Have you ever heard me complain?" he says. "I'm grownup enough to deal with it. It's part of the job and I've never been a darling of the press, ever."

Would you have liked to have been, just for a bit?

"Of course," he says. "It would be nice to be feted sometimes. During the Police, the press loved the Clash and the Pistols and Elvis Costello, but it's not really where the sparks are. My job as a musician is to be marginalised – and I certainly have been."

There is a song on The Last Ship called Practical Arrangement – perhaps the best moment on the record. A spare and delicate ballad, performed with Australian jazz singer Jo Lawry, it tells the story of an older unattached man trying to persuade a young single mother that they would make a good housemates. "I've no intention of deceiving you," he sings at one point, "you're far too clever."

In a way, that is the real Sting right there. Far too clever to be a pop star, but totally upfront about it. There was a time when anything he released was guaranteed to sell between 5m and 8m copies. The Last Ship, his first new album in nearly a decade, with guest spots from fellow Tynesiders Jimmy Nail, AC/DC's Brian Johnson and the Unthanks, may be more of a mental leap for such a wide audience. Occasionally, Sting sings in the sort of broad Newcastle accent he has never revealed before, the one he has previously felt placed him back in the small terraced street he grew up in, a place he once described as an "enclave of banality". There are times – as on the spoken word parts about Isambard Kingdom Brunel on Ballad of the Great Eastern – where the record veers dangerously close to Spinal Tap's "little children of Stonehenge" territory, but, you tell yourself, this is a story, not a series of diary entries.

"That navel-gazing that young songwriters get to indulge in is dangerous," Sting says. "Eventually it strangles you. I've certainly been paralysed by it in the past few years." Will it be a hit, I ask? Would he even like a hit?

"Oh, I'd love another hit!" he says. "It's fun to have a hit. But that hit would have to reflect me as a 61-year-old man. I'd find it demeaning, otherwise. Fame and ego and money can do terrible things. I know it's a cliche, but you still see people going through it. Look at Justin Bieber – it's like he's in freefall. I just hope he survives it because a lot of people don't. If I could give any advice to young musicians, it would be this: just try and enjoy it, because that truly explosive bit doesn't last for ever."

Sting's problem – if he could be said to have a problem – is that he is a fully functioning grownup locked in a relationship with an art form driven by a fetish for the young and the dumb, neither of which he has been at any point in his pop career. Fellow Geordie Neil Tennant has a theory that people are emotionally frozen at the age they become famous; so Michael Jackson was doomed to be 10 for ever, while Van Morrison will never shake off the part of him that is the grumpy teenager fronting Them. But Sting was already an erudite, articulate chap, a father, a 27-year-old, who had paid his rent and taxes and had other lives before any of this silliness happened. He knew what he was getting into. 79, when he'd barely had a hit, he told an interviewer, "My position is akin to that of a witchdoctor inciting trance-like barbarity."

"Well, I'm glad I had a proper job before this," he says now, fiddling with the engraved silver bangles on his left wrist. "I'm glad I was once a teacher with a pension plan and a mortgage."

Sting remembers as a child in the early 60s going to his friends' houses and being wildly impressed by the sheer number of books on the shelves. A few of them even had a car in a garage. One day the Queen Mother came to his street to launch a ship. Sting stood in his Sunday best waving a Union flag and as the Queen Mother drove past in her vast black Rolls Royce, she looked right at him and waved back.

"That was when I got infected," he says. "That was when I thought: "I don't want this life: I want that one. Once I'd found a guitar to play I found a friend to help me get there."

The fact that Sting did get there – doing what he wanted, in the way he wanted to do it – is no doubt why he appears so relaxed with himself and, it has to be said, so enormously likable. But it is also what makes his detractors infuriated ... envious, even. Maybe they think it's all been too easy for him?

"But it hasn't been easy at all," he says. "I worked fucking hard to make this all happen. I did the psychological work as a child dealing with unhappiness, insecurity and fear. And then that bore fruit."

And now, is he a happy man?

"Well, part of me thinks that happiness is a bovine concept," he says, getting up to leave. "Cows are happy, you know? On the other hand, it would be churlish of me to have even one complaint. I have had an amazing fucking life. If I'm not, who is?"

• The Last Ship is out on 23 September on Polydor.