Cinema: Lily-Rose - the next great Depp

Fast-forward almost 30 years, and the world is in a frenzy over a new Gallic adolescent with the same twiglet figure and insouciant pose.

Lily-Rose Depp is barely 16, and her appearance fronting a brand-new campaign for Chanel, lipsticked and trussed up like a Princess of Monaco has sparked a minor moral panic. Chanel has said that she is like a "baby doll." But at least one psychologist has expressed doubts about her debut. Child psychologist Dr Michelle Elliot said, "Sixteen-year-olds are not mentally, emotionally or intellectually able to cope with the pressures that these modelling situations place them in. I would not allow my daughter to become a model at that age."

The response of Lily-Rose's actual mother, Vanessa Paradis, to the hand-wringing is likely to be a knowing one. After all, she'd already been famous for two years by the time she was her daughter's age. Working for Chanel is almost like joining the family business - Paradis has a long relationship with the brand, having first modelled for it when she was 19, and last month she and her daughter appeared together on the catwalk for Chanel's Haute Couture show.

When the idea of her daughter following her footsteps was first mooted, she did express some reservations. "I started so young," she said some time ago of her time in the spotlight which has encompassed acclaim as an actress as well success as a singer. "I don't regret that at all and I really thank my parents for letting me do it. But at the same time, back then it was different - not that I'm 150 years old! And not that it was all safe back in the late 1980s. And now, being a mom, I don't know that I would have said yes." Still, she seems to have overcome her misgivings.

And why not? For Lily-Rose, stardom was not so much a choice as an inevitability. Partly, it's her genetic heritage - which is written all over her face. She's got her mother's high cheekbones, coltish limbs and delicate button nose. From her father, Johnny Depp, she inherited her almond-shaped, burnt caramel-coloured eyes. With genes like that there was never much chance of her slipping under the radar.

She is already a social media star. On Instagram, where she regularly publishes scenes from her fabulous life, she posted pictures of her recent 16th birthday party, for which she chose an unconventional "French Revolution" theme featuring, according to reports, peasants, swords and even a guillotine.

The presence of peasants was no doubt ironic. Lily-Rose's parents might have been born into ordinary families themselves (Depp's mother was a waitress and his father a civil engineer) but they have become showbiz royalty in their respective countries, and by having children together, it looks likely that they have launched a brand new dynasty.

And it's not just in fashion. Later this year Lily-Rose will make her big screen debut, having been cast in a major role, opposite her dad in the comedy horror film Yoga Hosers.

Certainly, her parents seem to be doing their best to keep her close as she makes her first steps into a public career. Perhaps even more so because the last few years have been challenging for the Depp-Paradis kids. Lily-Rose and her younger brother Jack have, in recent years, been dealing with the upheaval following their parents' break-up. Though officially announced in 2012, it's thought that the couple had already been living separately for some time before. Especially because it soon emerged that Depp was in a relationship with actress Amber Heard, 23 years his junior. The pair had met when filming The Rum Diary in 2011. Depp and Paradis spent over 15 years together and never married. But the actor tied the knot with his new love in February this year.

For many years, Depp's reputation as respected actor and adored celebrity seemed untouchable. Partly because of model looks and a certain softness in his eyes. He made his name in the 1990s playing a series of oddballs, outcasts and weirdos, none more memorably than his eponymous role in Tim Burton's Edward Scissorhands. This outsider quality seemed to fit with his personality - his early years of celebrity were rocky, a blur of heavy drinking, failed relationships and reports of a wrecked hotel room.

Globally famous before the age of 25 after being cast in 21 Jump Street, the attention sat uneasily with him. 'If the choice is to be gawked at constantly or to sit in a dark room, I'd choose the dark room,' he once said. 'When I was in a social situation, I was nervous and uncomfortable. The only way I could get through it was to drink my guts out! I wasted a lot of years.'

Romantically, he had a weakness for the renegades and the free spirits, first dating his Edward Scissorhands co-star Winona Ryder, and later, falling for supermodel Kate Moss. They were rumoured to be matched in their appetites. According to one biographer, Maureen Callahan, "Kate and Johnny were the chicest, druggiest couple since Keith Richards and Anita Pallenberg'.

Despite their common tastes, the relationship wasn't to last. "Johnny broke her heart," said Callahan. "She just wouldn't stop with the drugs and the drinking'"

It was while shooting a film in France that Depp first saw Vanessa Paradis. He later recalled in an interview the moment he first laid eyes on her. "She was wearing a dress with an exposed back and I saw that back and that neck, and then she turned around and I saw those eyes, and - boom!' . . . My life as a single man was done."

Physically they seemed like a perfect match - both were fine-featured and delicate. Her blue-eyed, candy-floss blonde looks seemed the ideal compliment to Depp's intense, soulful, dark ones.

Paradis was a stabilising influence. It was her, according to reports, who insisted he ease up on the drinking. For 14 years, it seemed that the actor had settled. Though he remained attracted to rebellious behaviour and renegade spirits, this found expression on-screen. He played a string of wild-men and outcasts, Hunter S Thompson in Fear And Loathing in Las Vegas, the Demon Barber himself in Sweeney Todd, and a debauched poet in The Libertine. Though none of this ragtag collection was more famous than Captain Jack Sparrow - his role as a troublesome pirate in the mega-franchise Pirates of the Caribbean.

By 2011, Depp was said to be worth $300m. "Basically, if they're going to pay me the stupid money right now, I'm going to take it," he said to Vanity Fair the same year. "It's ridiculous, yeah, yeah. But ultimately is it for me? No. No. It's for the kids."

Still, Depp seems to have got complacent of late. Previously known for his clever creative choices, he has, in the last two years, starred in two major turkeys - The Lone Ranger was a flop, swiftly followed by Mortdecai a spy comedy dubbed "a disastrously misjudged career low" for Depp. Several of his recent performances seemed phoned-in.

Perhaps it's about time for Depp to pass the baton to the next generation. Has Lily-Rose inherited a talent for acting as well as modelling? We won't have to wait too long to find out.