Moi Tarzan, toi Jane. If you visit the Eiffel Tower this summer, study the steelwork carefully, because you might see, or imagine you see, a familiar figure leaping from strut to strut. Tarzan of the Apes has taken up residence in the Musée du Quai Branly, the museum near the base of the Eiffel Tower, which is dedicated to non-Western – or, as some people insist, "primitive" – forms of art.

Paris may seem an unusual place to find the most learned exhibition about Tarzan, also known as Lord Greystoke, ever assembled. He was, after all, an English aristocrat and orphan fostered by socially responsible apes in the African jungle. He was the literary creation of an American writer, Edgar Rice Burroughs, who never bothered to visit Africa (and was so little steeped in African studies that his ape man wrestled tigers as well as lions). The museum has decided to de-construct the Tarzan myth as part of its mission to explore how popular Western culture understands, or misunderstands, non-Western cultures. Is Tarzan a sexist and a racist who subjugates Jane and treats black men like children? Is he a macho colonialist in a leopard-skin loincloth, rather than a pith helmet? Or was he the first ecological super-hero: a man in recyclable, locally-sourced clothes who fought to protect his pristine jungle from greedy commercial interests?

According to the curator of the exhibition, the celebrated French sociologist and anthropologist Roger Boulay, it depends which Tarzan of the Apes you are talking about. "There is a big difference between the original Tarzan of the Burroughs novels and the culturally impoverished Tarzan of Hollywood movies, starting with silent movies," he told The Independent. "The Burroughs character is complex and eventually speaks 12 languages. The movie character is often a caricature who speaks only in grunts."

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Tarzan's first spoken language, in the original novel of 1912, was ape-speak – long before scientists discovered that apes do have a language. The exhibition's catalogue contains a fascinating linguistic study of the words used by Tarzan's adoptive ape clan, "the Waziris". They have 250 words, including several verbs, which are used only in the infinitive, rather like George Orwell's Newspeak. It is worth noting that Tarzan's second spoken language in the original novel was French, learned from a French officer rescued from cannibals. Paris and the Quai Branly does have a legitimate claim to Tarzan after all.

The exhibition, which opens today and runs until 29 September, explores the many links between Tarzan and popular culture, especially the 80-plus Tarzan movies (far more numerous than the Burroughs books). Some faint praise is given to Johnny Weissmüller's series of 12 Tarzan films in the 1930s and 1940s and the indestructible eroticism of some of the early, silent films.

Overall, the exhibition suggests, Burroughs and Tarzan were ill-served by the movies until the British film Greystoke (1984) reverted more or less to the original story. The exhibition includes, however, a sequence from Greystoke in which Tarzan (Christopher Lambert) scampers in a convincingly ape-like way into the bed of Jane (Andie MacDowell). That incident is not in the original book, but eroticism has always been an important part of the Tarzan appeal. The exhibition makes comparisons with King Kong and the persistently engaging myth of the white woman kidnapped by apes.

Jane Parker, a scientist's daughter rescued from marauding apes by Tarzan, is a central figure in the first Burroughs novel Tarzan Of The Apes (1912). She then largely disappears and is replaced by a series of other girlfriends, some tough, some swooning.

The most celebrated chat-up line of modern times – "me Tarzan, you Jane" – does not appear in any Burroughs book, it transpires. It was first used by Weissmüller, a former US Olympic swimming gold medallist, in the film Tarzan And His Mate in 1934. The exhibition also has a magnificent collection of original plates from Tarzan comic books. These are jumbled, somewhat oddly, with authentic African spears and shields from the museum's own collection and a cuddly-looking stuffed lion.

Tarzan was "invented" by a science-fiction writer from Chicago who hated the modern civilisation that the city represented. Unlike, say, Rudyard Kipling, Burroughs never won acceptance as a great literary figure. The quality of his actual writing is often poor, especially in some of the later books among the 26 Tarzan titles. M. Boulay points out, however, that Burroughs at his best is far more than a mere writer of pot-boilers. His African knowledge was non-existent "but he was interested only in an imaginary Africa, for the needs of his story". His books are adventure stories but they have an intellectual background and purpose. "He explores the implications of the Darwinian theory of a common ancestor between apes and man," M. Boulay said. "He explores the failings of civilisation but also the failings of life in the wild. Long before ecological concerns became common, he has Tarzan defending the natural world against human predators."

Tarzan was an American "super-hero" two decades before Superman, Batman or Spider-Man were first drawn. But he was not "superhuman" or a mutant or dependent on tricksy technology. He gained his power by combining human cunning and wisdom with animal strength and endurance. "To that extent, he is a descendent of [the 18th century French philosopher] Jean-Jacques Rousseau, who Burroughs also studied avidly," M. Boulay said. "Rousseau believed that mankind, by straying from the natural condition, had forfeited part of his true character and strength."

So there you have it: yet another French connection with Tarzan. The exhibition is, in fact, subtitled Rousseau chez les Waziri. As M. Boulay points out, the Tarzan story is rooted in one of the most persistent myths in western culture, from Romulus and Remus to Rudyard Kipling's Mowgli. What makes Burroughs's Tarzan different from the other "children of nature", he says, is that the muscular ape-man swings between the jungle and modern, Western civilisation and back again. Tarzan goes home to England to claim his aristocratic title (and polish up his languages). He then decides to throw away his top hat and go back to Africa. He is torn between two apparently conflicting worlds and eventually unites some of the best qualities of both.

In his contribution to the exhibition catalogue, another French anthropologist, Pascal Dibié, argues that Tarzan, far from being a dated and risible figure in a loincloth, is a perfect hero for post-modern times.

"We are finally beginning to realise that we are, and always have been, part of nature," he writes. "There can be no doubt that nature must be the basis of our future civilisation and that the 'nature question' is the most important, political question of the 21st century. Tarzan, if he is still supple enough to grab a new branch, is far from dead."