I last saw James Thierrée flying upside down and making his body do things nature never intended, just after he’d fought a gravity- defying battle with an unsitdownable chair. So it feels somewhat odd to chat normally to this normal-looking chap, sitting normally on a normal settee as traffic shoots by along the Seine. The first question comes out all wrong. Does he, I kick off brightly with a furtive glance at his body, actually have a skeleton?

It seems a pretty innocent question to ask a bloke who has just turned 33, glowing with health, but it opens a can of worms. He positively winces. “Oh yes – and it’s really catching up with me. You know, when you’re younger, you think you can demand anything of your body. You’re elastic, immortal!” There’s a rueful grin as he flexes his muscles and rolls his shoulders. “All this hanging upside down, it gets more difficult – you start to feel your limits.” By my standards, Thierrée’s limits are still pretty mind-boggling but I am selfishly relieved that even Peter Pan might need a physio one of these days.

Thierrée is in Paris to launch his new show, which will then tour internationally, finishing in New York at Christmas. But first I want to get a word in edgeways about his upbringing, which sounds like something from a Boy’s Own tale. Born in Lausanne, Switzerland, in 1974, he learnt to walk at his parents’ circus based in Burgundy, surrounded by exotic beasts. He grew up in a caravan travelling the world as his parents toured their two-man show. When the rest of us were falling off bikes, he was mastering the trapeze – along with the violin, several languages and much else. Oh, and his grandfather was Charlie Chaplin.

Fighting back clichés about idyllic childhoods, I feel terribly earthbound. So where, if anywhere, was “home”? “I can’t say. I didn’t really grow up anywhere in particular, though we always came back to my dad’s family farmhouse in Burgundy. I guess over time ‘home’ became wherever I felt good, at ease – Italy, Australia, England. I don’t think of home in a staying-put kind of way.” He fizzes enthusiasm. “I have such wonderful memories of touring in the caravan when I was little. It’s wonderful for a kid, living in a little room with your sister, so exciting. The home, the centre, stays the same but it moves to different places and the decor changes every time you go out of the door.”

What about education? “When we went back to Burgundy, I sometimes went to school. But you can imagine what that was like, the feeling of being from outer space, all the other kids knowing you’re hardly ever there, you’re so different. Frankly, I don’t have great memories of school.” He brightens up. “On tour, we did lessons by correspondence. In the big towns, the cultural centres and the Alliance Française helped to find teachers for us. You know, you end up with a pretty good education because you cover the ground in far less time with one-on-one teaching.” Pause. “And just imagine being shut up in school all day long – what a nightmare!”

A free spirit, then, but with an illustrious heritage. Thierrée’s mother Victoria was one of Chaplin’s eight children by Oona O’Neill, daughter of the playwright Eugene O’Neill, and acted with three of her siblings – alongside Marlon Brando and Sophia Loren – in Chaplin’s last film, A Countess from Hong Kong. Others in the dynasty have also stuck to the performing arts – such as Chaplin’s youngest daughter, Annie, who runs a theatre.

Thierrée keeps the Chaplin link at arm’s length – after all, he was only three when “Charlot” died in 1977 – and is keen to stress his artistic independence. It has proved a handy defence mechanism, as those looking for similarities with grandpa find plenty to satisfy them, both physically and in the two performers’ distinctive mix of the burlesque and poignant. “Well,” he sighs philosophically, “at least it wasn’t the first question you asked me.”

Far more important has been the influence of his parents, Jean-Baptiste Thierrée and Victoria Thierrée Chaplin. “The circus phase didn’t last that long. My parents soon set up Le Cirque Imaginaire [later renamed Le Cirque Invisible] for the two of them, my sister and me. So this very diffused feeling of circus life – tents, animals, artists – quickly gave way to something more theatrical. Once I reached the age where you start to think about things, it was theatre that dominated.”

But wasn’t it hard to forge his own path away from such a tight-knit unit? And did he ever imagine a real job, the kind where people wear suits and read the FT? This gets a diplomatic chuckle. The mere idea of doing anything outside the artistic sphere has clearly never crossed his mind.

His first steps away from what he dubs the “protective cocoon” were in film, including work for Peter Greenaway (Prospero’s Books), Benno Besson and Bob Wilson, and as a stage actor. But although he still acts regularly in films, he soon gravitated back to the theatre/circus orbit and founded his own company, La Compagnie de l’Hanneton, in 1998. Hanneton means junebug, his parents’ nickname for him because he was always charging manically around the place.

The company’s first two productions – La Symphonie du Hanneton and La Veillée des Abysses – established a reputation for dazzling, eclectic acrobatic theatre infused with a dreamy aesthetic. The work was spotted in the provinces by Gérard Violette, director of Paris’s Théâtre de la Ville, where it is now a regular visitor.

Ironically, the company’s third show kicks off in a Parisian spring already packed with Thierrée-Chaplin productions. His parents are performing here for the first time in 30 years, while Victoria has just directed daughter Aurélia in the well-received L’Oratorio d’Aurélia. How many performing dynasties can boast three different shows in the same city within three months? “Mmm. I do hope people aren’t going to get fed up with us.”

Victoria designs costumes and accessories for both her children’s shows, which carry distinctive hallmarks of their circus and clowning heritage. James calls these props his “partners on stage” and structures his productions around fantastical interactions with objects ranging from railings to ropes.

Despite having a company of his own, Thierrée has steered clear of building a troupe of regular performers. His shows are his own conception and casting comes later, once the concept is already fleshed out and the all-important props have taken shape in his mind. Such self-sufficiency surely reflects his unusual childhood. “As a small animal, you understand that the set is changing, people are going to move constantly, so you make friends really fast and you don’t attach yourself to them too much.” Of course, such mobility has its downside. “You meet such a variety of people but you have always a sense that you have to be ready to leave and start afresh...it becomes a drug.”

The new show got a title only at the last minute and it’s even more bizarre than those of its predecessors: Au revoir parapluie ( Goodbye Umbrella). What on earth does this weird title have to do with the press blurb about the death of an old madman, loosely modelled on Orpheus pursuing Eurydice? “Aaah,” he says disarmingly, “not much really.” My eyebrows shoot up. “Well, it’s very hard to describe one’s own work. I had to give details so far in advance, you can’t possibly know how the show will evolve.” Fair enough – but where, I persist, did the peculiar title come from? Is the show a feel-good optimistic number – the sun will come out tomorrow? Or veiled pessimism about global warming, the end of rainfall as we know it?

He seems genuinely stumped, then rallies. “You know, I didn’t set out to make a trilogy or an open-ended series of shows like this. Now...well, people seem to like what I do and it would be terribly easy to carry on...but I don’t want it to become a brand, to get stuck in a rut. So the title is probably about me coming out from behind my own shelter, launching into the unknown.”

What might that be, I ask eagerly. He hates being labelled or pinned down but owns up to a growing passion for directing. “I’ve been getting closer to theatre, the need to tell stories. And now I think I would love to make films – not mainstream ones, you understand, but out-of-the-box films, crazy, imaginative.” The Chaplin name might be a little bit useful if you want to go into film, I tease him. He has the grace to blush.

Thierrée’s joints may be causing discomfort but he still bounds where the rest of us plod. He leaps off into the spring sunshine to drive out of Paris before the rush hour. Where are you off to for the weekend? I call after him. “Burgundy – I’ve got to blitz props with my mother.” Now, there’s a surprise.

‘Au revoir parapluie’ opens on May 16 at the Théâtre de la Ville, Paris. Tel: +33 1-4274 2277