Jake Gyllenhaal may be of Swedish descent, but his inner chef is definitely French, his costar in Source Code tells PEOPLE.

“Jake’s an incredible impersonator with great accents,” Michelle Monaghan said at the film’s world premiere at the South By Southwest Film Festival in Austin, Texas, this weekend. “We shot in Montreal, and [off-set] Jake played this sort of old, funny, French foodie chef – and talked a lot about food, because we ate a lot there.”

Monaghan, who plays a woman Gyllenhaal is trying to save in the sci-fi thriller about a man who occupies other people’s bodies for the final minutes of their lives, says she had a lot of fun with her costar – despite the serious nature of the film.

“Jake’s really, really funny,” Monaghan, 34, says. “And I’d never seen that side of him in his films. To have the opportunity to spend time with him was so much fun. He’s fabulous.”

Of course, Gyllenhaal, 30, has a serious side, as well. Talking about his character, the actor shared his thoughts about what he would do if he were given the opportunity to cross over to another man’s identity – and it has nothing to do with French cuisine.

“If I were to go into someone’s body whose life I felt was cut too short,” he said at the premiere, “there are a number of circumstances I can think of. In fact, it’s kind of hard right now to be at a movie premiere at a festival when you think about what’s going on in Japan. To be able to change things like that.”

Gyllenhaal continued: “Or how great would it be to be able to go into Martin Luther King’s body? And to be able to tell him: ‘Don’t do this. Don’t go there.’ That would be an amazing opportunity.”