If The Killing's Sarah Lund set down the marker for a new breed of TV detective who is female, troubled, dogged, idiosyncratic, often unsympathetic and occasionally irritating, then the character of Saga Noren was its next most significant milepost.

Noren features in The Bridge, a Danish-Swedish co-production from 2011 which turns on a joint police investigation into a killer who places his first victim on the span separating Copenhagen and Malmo, and then continues to pick off those who have offended his political sensibilities.

Played by Swedish actress Sofia Helin, Noren takes Lund's troubles and idiosyncrasies and raises them by adding a sports car and what appears to be a form of autism, possibly Asperger's syndrome. She finds empathy difficult and abruptly propositions men in bars. Nor does she think anything of changing her clothes in her open-plan office in full view of her colleagues or looking at grisly images of murder victims while in bed with a one-night stand. When people skills were handed out, she wasn't even in the queue, and she's treated with a mixture of bemusement and frustration by Martin Rohde (Kim Bodnia), the amiable Danish detective she teams up with to crack the case.

A second series of The Bridge is currently airing in Denmark and Sweden. Meanwhile a 13-episode American remake, set on the stretch of border between El Paso in Texas and Juarez in Mexico, has just finished its run on the FX network in the US. It features Demian Bichir and Diane Kruger (who bears an uncanny resemblance to Helin) as the odd couple detective team. A second series has now been given the green light. Not to be outdone, Sky Atlantic and French channel Canal Plus have teamed up to make their own 10-part version, commissioned from Elizabeth Murdoch-owned production companies Kudos (makers of Broadchurch) and Shine France.

Lack of a connecting bridge or an easily crossable border has proved no impediment, either. This new version is called The Tunnel, and its crucial opening scenes take place in the Channel Tunnel, exactly at the mid-point between the British and French jurisdictions. It stars Stephen Dillane and Clemence Poesy as Karl Roebuck and Elise Wassermann, British and French respectively, with Dillane's Game Of Thrones co-star Joseph Mawle in a supporting role alongside Keeley Hawes. In a rare concession on the part of Sky Atlantic, the plentiful French dialogue is subtitled, though because it's clearly beyond the limits of credulity to have an English policeman who speaks French, Wassermann speaks fluent English (virtually unaccented too, thanks to Poesy's run in the final three Harry Potter films).

Director of the first two episodes is Franco- German filmmaker Dominik Moll, an arthouse favourite thanks to festival hits such as Lemming and the Hitchcock-influenced Harry, He's Here To Help. This is Paris-based Moll's first foray into television but he was attracted, he says, by the growing realisation that small-screen drama is the ideal place to examine the lives of complex characters and to explore their contradictions. Not for nothing has he long cast admiring glances at American series such as Mad Men, The Wire and The Sopranos, which do just that.

"I felt there was room for me to do something with the characters, to create something that was also close to me and not just do a directing job on some series," he explains. "Also the fact that I was offered the chance to direct the first two episodes, and set up the tone and make all the major choices about casting and locations, that was also very rewarding and interesting for me … It was never a question of making things better or improving them, but just seeing the possibility to create a variation on that same theme and that plot."

One of the most significant changes made by Moll and scriptwriter Ben Richards is to the character of Wassermann. Where her oddness is made explicit in the original Scandinavian production, Poesy tones it down. She still strips off in police headquarters and propositions a stranger - two memorable scenes that no self-respecting adaptor would be without - but otherwise she functions more or less normally.

"It was deliberate," says Moll. "We didn't want her to have a defined pathology. If you really want to say she has Asperger's, there are things [that go with it] such as being physically very clumsy, which she isn't. So if you do it seriously, you have to integrate all parts of it. We thought it was more of a limitation than anything else and what Ben Richards wanted to concentrate on was her relationship to the truth. She's someone who doesn't cheat with the truth and doesn't understand why someone would. She's just very direct and rational and all her behaviour is organised round that."

Giving The Tunnel its distinctively British flavour is Stephen Dillane's sardonic portrayal of hardbittern cop Karl Roebuck (recovering from a vasectomy operation as episode one starts, as in the original series) and Moll's emphasis on the bleak countryside and delapidated Kent towns in which much of the action takes place. The palette Moll and his director of photography have chosen - an array of cold greys and muted browns - takes its cue from the opening scenes, which were shot inside the Channel Tunnel itself, though not at the official mid-point: as Moll observes, once you're a mile in, it all looks the same.

"Our starting point in the discussions was really the tunnel. To be able to start the series there was really something, a real treat. It was great not only because a tunnel is always something that stirs someone's imagination and fantasy because it has to do with the unconscious - you don't know where it will come out - but also because the colour palette was very limited and dark. The only colour is the yellow signs and doors, so we took that as a starting point and tried to give the rest of it the same kind of feel, of something dark but with character."

Game of Thrones star Joseph Mawle plays Stephen Beaumont. We first meet him in the opening episode ministering to a young female immigrant who is being coaxed into prostitution by a local thug. We learn later that the same man is involved with Beaumont's sister, Suze (Hawes) and knew one of the murder victims. Predictably, he's well known to Roebuck.

"Stephen has a deeply rich past but the whole point about him is that he doesn't reveal much at all," says Mawle. "He's deeply complicated but also has his motivations and his reasons for doing what he does - but to explain them would be unhelpful to the audience's enjoyment of a drama like this, which is one that is going to challenge and not offer every answer at every step of the way."

Unlike Moll, who watched the original series, Mawle has avoided it - as have The Tunnel's Gallic audience, who won't get to see either The Bridge or the US remake until after The Tunnel has aired. In a bid to stop spoilers, Canal Plus have bought the French broadcast rights to both series.

"There was a temptation to watch it, because I know the Scandinavians made a staggering job of it, but I think you have to just stick to your guns when you get a script and interpret it the way you see it and the way you and the director work through it. And Dominik Moll was one of the big draws to the project for me: he's a film director, and he has a film eye and he thinks in a film way, and that's very appealing. It's something I'm more and more interested in."

Quite what the Scandinavians will make of it remains to be seen, though by now the Swedes and Danes are well used to the best of their exports being recast for international audiences. Even Borgen, which dealt specifically with the office of the Danish prime minister, is reportedly being given the remake treatment by the American network NBC - ironic given how much Borgen's creators were influenced in turn by US political drama The West Wing. A third series of Borgen airs on BBC Four early next year, where it will be joined in the schedules for series two of The Bridge. But for those who can't wait, The Tunnel's noirish, Franco-British twist on it will more than kill the time.

The Tunnel starts on Sky Atlantic on Wednesday