A new documentary, John McEnroe: In the Realm of Perfection, has been called, in US Vogue, “the best tennis film ever made”. This in itself is not necessarily the greatest praise you could heap on a work of art: it is like calling a footballer “the greatest English left-sided midfielder of the 21st century”. But the writer goes even further and nominates it as “among the very best films on any sport that I’ve ever seen”.

That, for me, is a stretch. In the last decade there’s been Senna, Free Solo, Icarus and, if you’re loose with your definition of a sport film, OJ: Made in America. But In the Realm of Perfection does do something powerful and meaningful. It takes an individual you thought you knew inside out and makes you look at him anew. This really is McEnroe as you have never seen him before.

That is down to the footage and there is a neat story here. In the Realm of Perfection has been made by a Frenchman, Julien Faraut, whose day job is as an audiovisual archivist at the National Institute of Sport in Paris, where he is responsible for the 16mm film collection. A few years ago, a friend of Faraut’s started work on a project about Gil de Kermadec, France’s first and longtime national director of tennis. In the course of helping his friend, Faraut found a huge trove of John McEnroe footage no one knew existed. It was all shot at Roland Garros between 1981 and 1985 when McEnroe was at his peak as a player. “This kind of material is very rare,” Farault has said. “Most of the time, it’s destroyed.”

Of course, there is plenty of match footage from that era already, waiting for a rain break in the live coverage, if the French have that tradition. But the action that De Kermadec obsessively hoarded was different for a few reasons. One, it was shot on 16mm film, giving it a textured, sun-dappled cinematic aspect that is more stylised than footage from regular TV cameras. Another deviation was De Kermadec often followed matches with three cameras, including one in “the pits”: a foxhole behind the players, about level with their calves. And the last major difference was De Kermadec asked his camera operators to solely track one player, not the match.

This viewpoint will be familiar already to sporting cineastes. It proved to be unexpectedly enthralling in Douglas Gordon and Philippe Parreno’s 2006 film, Zidane: A 21st Century Portrait, for which 17 cameras followed the midfielder over the course of a Real Madrid match against Villarreal. But what, then, do we learn about McEnroe from the unearthed footage?

Well, we find the Superbrat at his most irascible, for one thing. Part of the reason for that is actually directly connected to De Kermadec himself. “One of the cameras,” Farault has noted, “shot more quickly than the others and made a very annoying noise during silent rallies.” This incensed McEnroe – not without justification, you have to say – and it becomes a recurring drama throughout the film. He also became infuriated with an invasive boom De Kermadec’s sound recordist held, at one point snapping: “Keep that thing away from me, you understand?” He then gestured to his racket: “See this? In your mouth.”

There are a lot of tantrums in John McEnroe: In the Realm of Perfection. Some are a response to noises or flashes, real or imagined; many more are directed at incompetence, again real or imagined, by officialdom. These outbursts are so heartfelt and theatric that, at one point, Farault overdubs the action with audio from Raging Bull, the scene where Robert de Niro’s Jake LaMotta accuses his brother: “You fuck my wife?”

It is clearly Farault’s hypothesis that McEnroe drew strength from these outbursts. He used his perceived persecution to rouse himself to greater efforts. Whether he realised his behaviour could also distract or intimidate his opponents, who would often subsequently lose their momentum, is unclear. Certainly, it is a high-wire strategy: very few players in any sport can genuinely lose their rag and be confident it will improve their performance. The only modern equivalent in tennis is Novak Djokovic, who sometimes appears to thrive when he is convinced most of the stadium is willing him to lose.

The perfection McEnroe is searching for in Farault’s film is his first title on the Paris clay. Most of the action in the documentary is drawn from 1984, when the American was in the midst of the most successful season enjoyed by any player in the Open era. OK, “enjoyed” is not the right word; McEnroe mostly seemed furious, but it drove him to a still-record 42-match winning streak that landed him in the final at Roland Garros against Ivan Lendl.

Now, McEnroe really wanted to win the French Open: he had already won Wimbledon twice, the US Open three times, so – in the years before the Australian Open was contested by all the best players – it was the major gap on his CV. He also really did not like Lendl: the Czech played without guile or finesse, McEnroe’s defining qualities. And, on that day in June 1984, the gulf in talent seemed immense as McEnroe sprinted to a two-set lead in scarcely an hour.

But it was not to be. Lendl doggedly pegged back McEnroe; the American took a 4-2 lead in the fourth set but could not finish him off. It went to a fifth and Lendl powered through 7-5. McEnroe was so distraught he would not, or could not, speak to the crowd. He was roundly booed as he walked off the court.

In a way, McEnroe’s defeat is like Don Bradman failing to get a 100 run career average in his final innings. It is the Persian rug with a deliberate mistake. Again, it is not obvious that McEnroe himself feels that way. Apparently, the defeat in 1984 has haunted him ever since. He still cannot shake it when he goes back to Roland Garros to commentate. How could he, playing near-faultless tennis, fail to win a tournament that has latterly been won by journeymen such as Ecuador’s Andrés Gómez in 1990 or the Argentinian Gastón Gaudio in 2004?

So a year when McEnroe lost three times, when he triumphed in 96.5% of his matches, was ultimately tainted. Sport can be brutal like that. The film sums it up neatly with an observation from the director Jean-Luc Godard: “Cinema lies,” he once said, “sport doesn’t.”

In the Realm of Perfection is released in UK cinemas on 24 May