She's certainly done her homework, seeing the original film and reading the book. "That old Steig was drinking some espresso!" she exclaims. "Wow! He has so many layers." When we meet, she's just seen Fincher's version and is full of praise for her fellow cast members - the "affable, adaptable" Daniel Craig, who plays Blomkvist, and newcomer Rooney Mara, who made a brief appearance in Fincher's Facebook movie The Social Network, before landing the plum role of Lisbeth Salander. "She's a great little actress. She's going to skyrocket."
She reserves most of her praise for Fincher (with whom she looks set to reunite on his next project, a television reworking of the British political thriller House of Cards). "Fincher was very loyal to the book but I think his talent is where he chooses to show you, the audience, intensity without too much exposition. So it's almost like an aria when you watch it. The Swedish film was staccato - every single scene that was in the book and every single character, you got little flashes to get all the information. And his aria is ... he's a master at film-making for that reason. He knows where to pump up the volume and where to subside, and let you imagine. You wonder at a lot of the movie ... you're not quite clear where it's going."
Rampart is no less intense than Dragon Tattoo. Set in Los Angeles in the late 1990s, its title refers to the Rampart scandal, where widespread corruption was uncovered in the LAPD's anti-gang unit - not least three officers found on the payroll of hip-hop mogul Marion "Suge" Knight. "Being from Los Angeles, we heard about it," says Wright. "It was on the news. It was the OJ times, and Rampart - a beautiful time to live in Los Angeles. The 'city of corrupt' is what we used to call it."
Neither was she immune: in the mid-1990s, she was robbed of her car at gunpoint in Santa Monica, inspiring her and Penn to move out of Los Angeles to San Anselmo, 20km north of San Francisco.
Scripted by James Ellroy, the film sees Woody Harrelson play Dave Brown, a disturbed, trigger-happy cop who is caught on video beating a luckless driver who accidentally rams his car. It's Harrelson's film, a fierce, unflinching Oscar-nominated turn if ever there was one. Wright plays defence lawyer, Linda Fentress, one of several women in Brown's chaotic orbit. Having known Harrelson for 17 years, playing his lover didn't come easy. "We're like brother and sister. So it was like incest!" she cries. "We talked ... [I said] 'I can't do love scenes with you, Woody!' He's like [she adopts a credible Harrelson-like twang], 'well, you know, I guess it's like you're going to have to be my hot sister'."
Since completing Rampart, she's been to Germany to film Waltz With Bashir director Ari Folman's new film The Congress - a mix of live action and animation - though she's something of an anglophile, if truth be told. Her stepfather was from Cheshire - "Wilmslow to be exact" - which may explain why Wright frequently breaks into an English accent in her answers. "I had to perfect it, because if not, I would be basically whipped. He would correct us all the time." Turns out, he's even influenced her choice of football team. "I'm Man United," she beams. "My dad was a Stretford End regular. Eric Cantona - he was amazing."
Wright had her own stint in Europe, during her modelling days, before she returned to the US to start acting - first in commercials and then in daytime soap Santa Barbara. Later came cult movies (The Princess Bride), enormous hits (Forrest Gump), and forgettable fare (How To Kill Your Neighbour's Dog). "I've been told I've done a lot of flop movies. And I think, 'wow, I've never considered them flops'. I've loved every character I played. They bring up [Barry Levinson's 1992 comedy] Toys. I had such a blast playing that girl. Got to create her on my own. That's what it's about. Make it fun and fulfilling - for yourself, if nobody else."
Ironically, The Congress sees Wright play an actress whose career has waned after the studios have endlessly re-used her image. In reality, partly because she never really let the studios do just that, she's survived into her 40s (she's now 45) - difficult when the options of "what's available to you, given your age and lack of Botox" become less and less. It's not hard to sense that she feels on borrowed time. "You go 'okay, we've only got a couple more years' - which is a reality in Hollyweird."
Even so, Wright feels that things have changed since her days as an aspiring soap star on Santa Barbara. "I feel like we're almost programming audiences to this," she says, stretching her cheeks back into a smile, "and they're getting used to it. So maybe the time is limited for us, if we're not going to go down that path. So your roles are different. They're definitely shifting."
In her eyes, "The seasoned woman is going to offer a more seasoned character." Which may account for why she's having the time of her working life right now.
Lowdown
Who: Robin Wright
What: The Girl With The Dragon Tattoo
When: Screening now
-TimeOut / Independent