Jean Reno looks a bit upset when I tell him that I don't like interviewing actors. Admittedly, insulting someone's profession is not a classic opening gambit. It can't be in the Michael Parkinson Guide to Good Interview Practice, certainly. It probably wouldn't even be sanctioned by the Fearne Cotton School of Free- Association Chats with D-listers. Nonetheless, I find myself sitting opposite Reno in an Edinburgh hotel, involuntarily declaring that members of his profession usually make for bad interviewees.

He fixes me sombrely and frowns. Or at least I think he does – anyone familiar with Reno's vintage performances in the films of French auteur Luc Besson, or his turns in Hollywood blockbusters such as Mission Impossible and Ronin, will know that part of his melancholic charm lies in that wonderfully sombre, frowny face.

It's because, I say, they tend to be naturally entertaining, so it's only on the way home that it dawns that they have, for all the charming conversation and apparent intimacy, told you virtually nothing. I hold my breath and hope he takes it as a compliment. '

Reno nods slowly. "Ah oui, I understand," he says in his heavily accented growl. Reno isn't a smoker, but if a packet of Gauloises could talk, this is probably what it would sound like. "It is an actor's defect. I want everybody to like me, so I'll say what I think will please them. But there's also the opposite. Those who are a little ashamed of what they do. Like this..." He withdraws into his chair, eyes closed, tersely clutching his forehead and doing an excellent impersonation of Hugh Grant in full why-am-I-promoting-a-romcom-when-I-could-be-fighting-for-my-country mode.

"I think it's because acting, the imitation of life, is not really a natural thing to do," he continues. "It wasn't that long ago that the church refused to bury actors, you know? At the end of the day, you are a kind of performing monkey."

Today, Reno doesn't correspond to either archetype. Despite his auto-critique, he is more reflective than your average people-pleaser, pausing often to consider a question, struggling for the correct English. We're meant to be talking about his latest film, the French-language crime flick 22 Bullets, but Reno is clearly not one for the hard sell. If anything he seems happier on topics usually strictly off-limits – family, relationships, celebrity pals.

The previous night, he tells me proudly, he celebrated his teenage son's exam results by taking him to see AC/DC in Paris with his mate Johnny Hallyday. There is some kind of legislation in France, it appears, which means all famous people have to be friends – Hallyday shared best-man duties at Reno's 2006 wedding, to his third wife Zofia, with none other than one Nicolas Sarkozy.

Reno tells me they (he and Nicolas, that is) met while walking their dogs each night near their then-homes on Paris's Ile de la Jatte. "It was a bad time for both of us. He had broken with Chirac and was really down in his party, completely abandoned. I was about to get divorced. We'd go out for the nightly promenade and talk. I don't see him so much these days; he's pretty busy," he chuckles.

In career terms, too, Reno, now 62, is a difficult specimen to classify. My initial nerves are, I think, partly due to the fact that this is the man who has turned in some of my favourite performances, in my favourite films – as the macho but hopelessly sentimental Sicilian diver Enzo in The Big Blue in 1988, then in 1994's Léon, as the eponymous hitman who guilelessly embarks on a strange platonic love affair with a pre-pubescent Natalie Portman. Both were under the direction of Besson, and both demonstrated Reno's ability to effortlessly marry those elements – comedy, violence, tenderness and vulnerability – that overlap all too often in life and not often enough in its representation.

Then again, this is the same man who has appeared in some of Hollywood's lamer efforts of recent history. Couples Retreat, anyone? The Pink Panther? The Da Vinci Code? I look over his filmography to refresh my memory and am dismayed to see he went back for more with The Pink Panther 2. His is a schizophrenic CV, to say the least. As far as I can tell, Reno is never bad in a film, but he is certainly in a fair number of ropey ones. Alongside the American blockbusters are plenty of solid French-language movies, a mixture of comedies and policiers.

His latest belongs in that final category. Reno plays Charly Mattei, a Marseille gangster who is trying to go straight when he finds himself riddled with bullets – the 22 of the title – by his former gangland buddies. Somehow he survives and a slick revenge tale ensues.

It's based on a true story and perhaps aspires to the success of 2009's Mesrine, in which Vincent Cassel portrayed France's most notorious criminal. It lacks the graphic, messy honesty that made Mesrine such an interesting proposition, but it's a decent, pacy thriller. Does Reno, who has played innumerable killers and mercenaries since Léon, never get bored of dispatching fellow cast members for a living?

"I think it can be quite hard to do violence convincingly, harder than you'd think maybe, so once people know you can do it they keep coming back. But, to be honest, I'm not one of those guys who's fascinated by guns. That's why I like to do a lot of comedies in France. I don't get the romances. I did try – a film called Roseanna's Grave in the 1990s. I liked it. But the audience didn't come."

He appears sanguine about this fact, as well he might, given the success he has enjoyed playing hitmen. On an international scale, Reno is probably, alongside Gerard Depardieu, France's most recognisable working actor. Though when I mention this, he corrects me: "Gerard doesn't really work any more, he has terrible trouble remembering his lines." Given that Depardieu admitted to being fed his lines via an earpiece for a stage production as long ago as 1994, things must be bad. On top of which, a poll in France earlier this year named Reno as the country's favourite actor. Depardieu didn't even make the top 10, which was filled largely by actors whom anyone without a keen interest in French film is unlikely to have heard of – Danny Boon and Jean Dujardin, for example.

But despite his popularity with the public, Reno says he is not held in great esteem by French critics. Like Depardieu, he has been accused of selling out: "J'ai pas la carte – I'm not a proper member of the establishment, you know? Oh, they gave me all the medals and the honours, but I'm not on the inside.

"In France, if you have any sort of talent, you'd better keep it here. And if you're going to go abroad, it had better not be America. The old battle – American versus Frog cinema. It's ridiculous. So if you're a good tennis player, you're not going to go to an international tournament? "What I want to know," he ' continues, very animated now, "is why then, in France, the Centre National du Cinéma [a publicly owned body regulating and supporting cinema] takes a little money from each cinema ticket sold, including all those for American films, and uses it to help young French directors. It's hypocritical. And it's so typically French."

I see his point, and wonder whether I'm just being a film snob too, but I can't help feeling that it's not simply that Reno chooses to do American blockbusters, it's that he chooses to do quite a lot that is dross even by Hollywood standards. "OK, Ronin was quite good and Godzilla wasn't bad. But, er, Couples Retreat, Jean!" is what I want to say. But sitting in front of him, I think he genuinely believes that these are all decent, commercial films. And so – apologies – I skirt the issue by asking whether he finds the quality of his Hollywood roles is limited by his nationality.

"I have a strong accent; it limits the roles, of course it does," he says, unchippily. "I guess if I had moved to America a long time ago maybe my accent would have got less. But for me to dream about being the next Steve McQueen or a George Clooney, it would be fantasy... The population of America is changing, though, the Hispanic population is growing. So maybe that will change too. But not for the moment."

Ironically, for all the deep-thinking/dodgy Frenchman roles he gets in US films, Reno doesn't consider himself terribly representative of his nationality. Born in Casa-blanca, Reno's Spanish parents moved to Morocco from Andalucia in the 1940s, when many Spaniards were starving under the Francoist regime. He moved to France at 17, but says it is his Andaluz heritage that defines his character: "The melancholy is the Andalusian in me. My father gave me that. It's an awareness you are going to die. It's not sad; it helps, in fact. When you are unhappy, you drink, you eat, you listen to a little flamenco, the black sounds. It reminds you to live."

It is perhaps this that endows him with a soulfulness that makes all of the characters he plays – from killers to two-dimensional caricatures – more intriguing than they might other-wise have been.

I tell Reno that during my research I found a very serious academic article describing him as a new genre of action hero in American cinema, complete with an analysis of his character's relationship with Robert De Niro in Ronin, as a metaphor for power relations between France and the US. He laughs heartily at this, clearly amused to be the focus of such grand theory. OK, then, I ask, what is he proud of in his career?

"Oh, I don't know. I hate looking back, it gives me a pain in the neck," he shrugs. But he pauses, thinking. "It's hard for me to remember my films the way they end up being in the cinema – I remember them how we made them.

"So for me it's moments on set, simple things – the first time you all get on set, the first time you do a read through. Like with Ronin, I remember the first time we were all together. Looking around at Natascha McElhone, Stellan Skarsgard, Sean Bean – ouf, Sean Bean, he was very mean! – then Bob. Thinking 'Robert De Niro! What's he doing here?'"

That Reno loves the business of making movies is obvious. With every film he mentions, he recalls the various nationalities of the team who worked on it, a little anecdote from filming, with visible pleasure. "I came to acting because I wanted to be with people," he tells me, and though it's a crude psychological appraisal, it would make sense for a man who grew up between several cultures to feel at home in the itinerant world of the film set.

But I get the feeling that Reno prefers making films to watching them – certainly his own, anyway. After he has done his scenes, it's on to the next with no time for retrospective analysis. Nothing wrong with that necessarily; in fact, it seems pretty natural – otherwise he'd have been a film critic – but it might explain the variable quality of his projects.

Though he says it's too early to talk about, Reno tells me that he's in talks to do something on the London stage in 2012. His career began in the theatre, and he has interspersed his film work with the occasional play in France, but it will be interesting for those of us who have come to know Reno via the screen alone to see how he fares live on stage.

I've been warned that Reno doesn't like to talk about his old Besson films, but I'm damned if I'm leaving here without talking about Léon. For many, it remains Reno's best work and I want to know what he thinks of it these days. Given his largely mainstream choices since, and our increasingly hysterical fears around paedophilia and the sexualisation of children, I wonder whether he would take on such a film now.

"I don't know. You know that scene where I give Natalie the dress and she comes back in wearing it? I kept saying to Luc we have to rehearse that scene, and he kept saying, 'Yes yes yes, wait, we'll rehearse it.' It was never rehearsed, because in fact he knew I didn't want to do that fucking scene at all."

He doesn't elaborate, but I know what he means. It's in that scene where the thin line between the behaviour of a surrogate father and that of a lover is most keenly felt.

"I would do it again, because it was extraordinary," Reno says firmly. "When we all watched the movie, we cried a lot. We knew we found something special"

My time with Reno is up. Have I changed my opinion of actors and interviews? Well, I liked him. And he was certainly more candid than your average film star. After all, who knew Sean Bean was mean?