Lucy, a loopy blast of kinetic energy, is perfect modern multiplex fodder. There's eye candy (a lot), brain food (a bit), an ass-whupping antiheroine (an abundance thereof), and an 89-minute running time that means you can still fit in a Jamie's Italian before bedtime. In other words, it's a welcome return to the Luc Besson of the 1990s.

Playing on the old myth that we use only 10% of our brains, Scarlett Johansson is the partying student and reluctant drug mule who becomes an action hero, then superhero, as the narcotics involuntarily stuffed in her stomach seep into her bloodstream, that 10% rising rapidly to 100%. The film hurtles along as her brain goes full-throttle. The drug, says Besson, is inspired by "a molecule that pregnant women create after six weeks – a super atomic bomb for a baby". He knows the 10% brain capacity theory is hokum. "What's true, though, is that we only use 15% of our neurons at the same time," he says. "But it's never the same 15%. So we can ask ourselves, what happens to us if we can suddenly have 30%, 40%, 50% of our neurons working at the same time? I changed the reality a little to help the story."

As a director Besson has had an iffy 21st century, and Lucy, while not his best, is a good reminder of why he made such an impact in the first place. 1988's The Big Blue was a plaintive, pretty paean to his love of deep-sea diving, but 1990's Nikita introduced Besson as a turbo-charged action director: with Anne Parillaud as a murderer-turned-spy, it boasted a no-nonsense female shit-kicker a year before James Cameron brought us Terminator 2. Besson went bigger and better with Léon, giving Natalie Portman her first role as a 12-year-old apprentice assassin in love with a taciturn middle-aged hitman; then he went huge with The Fifth Element, an arty, bonkers sci-fi featuring an arty, bonkers alien (Milla Jovovich). The French critical consensus was that he was a crass sell-out in thrall to Hollywood; Hollywood welcomed him with open arms.

Tonally, Lucy is Besson in a blender, with shades of both The Fifth Element's sense of desperation and wonder, and the gung-ho, wham-bam spirit of the Taken/Transporter/Taxi films he's spent the last few years writing and producing. Not that he agrees. "When I make a film I'm not even thinking about anything else," he says. "Lucy is the first time I've taken a character who is totally normal at the beginning of the film. She's Miss Nobody. She's studying, she's partying too much, she doesn't know what to do with her life; a totally average girl. Most of the time I start with amazing people, like Aung San Suu Kyi [in The Lady], or [Fifth Element's] Leeloo. So for me, she is totally different from anything I've done."

Lucy puts every man in the film in the shade by several degrees. It's a Besson motif: the scripts he writes for others may be testosterone-heavy but the majority of those he keeps for himself feature headstrong female leads. Again, he dismisses the idea: "When I started to think about Lucy nine years ago, I knew the film would be for me, but I didn't know the protagonist would be female. It's more than whether it's a female. If I think another director could miss the point, I don't want to give it away."

He's certainly happy to give away his brawnier ideas. His Jason Statham/Liam Neeson vehicles – less idiosyncratic and less conceptual than the films he directs – have proved lucrative for his company, EuropaCorp. Those are Besson's franchises, and onwards those juggernauts roll. The Transporter is currently being rebooted, while the third Taken film wraps two days before we speak. He initially said that Taken would be a one-off. After the sequel, he said, OK, really this time, that's it. Money, presumably, changes his mind: the first film cost $25m and made $227m, while the second made $376m.

Business aside, these movies clearly work. The Taken films hit home, says Besson, because they play on parents' fears for their kids and, at the same time, provide wish-fulfilment. "Every dad dreams about being Bryan Mills, and every daughter dreams of having Bryan Mills as a dad," he says, and he justifies milking the conceit. "After the first one, I couldn't see how we could do a sequel. We decided to do a continuation of the first one. The first one the girl is taken, the second one they take vengeance. It's one story. The third one is an original. It's the same family, but nobody is taken. The dog is not taken."

One assumes money is a big factor in the films he doesn't direct, but he's more protective over those he does. He refuses to follow up The Fifth Element, and, thankfully, hasn't given in to those demanding a Léon sequel. "You can't imagine how many people ask me for a Léon sequel," he says. "Everywhere I go they ask me. If I was motivated by money I would have done it a long time ago. But I don't feel it."

The hitman and her: Jean Reno and Natalie Portman in Léon. Photograph: Allstar/Cinetext/BUENA VISTA

The longer we talk, the deeper Besson is keen to get, assuring me the appeal of Lucy as a project was philosophical. "What's interesting is the definition of humanity," he says. "Watch the news tonight. When you see the state of humanity today… I mean, come on, it's a mess." Lucy's message, he says, is that when you have power, the best thing to do is to share it. When I ask what sort of films he's burning to make, he says how much he values the purity of children over adult cynicism, and would like to do something with that.

People tell him, he says, that he's a big kid himself, and his parents' divorce, when he was 10 years old, has influenced his career. "Here is two families," he once told the New York Times, "and I am the only bad souvenir of something that doesn't work. And if I disappear, then everything is perfect. The rage to exist comes from here."

Does he still feel that rage?

"No, I don't have it any more," he says, confessing that film-making is therapeutic.

"You have a suitcase full of souvenirs and trauma, and when you're young your suitcase is always open. When you become an adult you learn how to close it, and to open it when you need it. And that's what I learned. So I always have my suitcase, with all my scars. But I can live with it. I can handle it. And when I write or direct a film I open it, I use it, and then I close it! I'm not bothered by it any more. But you don't forget it. It's nice to have a suitcase."

Lucy is in cinemas from Friday

• First-look review: Lucy

• Lucy's US box office