They play two young New Yorkers in The Disappearance Of Eleanor Rigby, and its writer and director Ned Benson said casting McAvoy as Chastain's husband was "a dream".
He said: "He's hilarious and silly and charming, but he's also a searcher. He works really hard and wants to find the scene and will constantly push through each take to sort of ask a lot of questions.
"He really wanted to get to the epicentre of what the scene was about. For me he was the guy that could make me feel relaxed at all times because he was so relaxed."
The film is not in the running for the festival's prestigious Palme d'Or award, but is shown as part of the Un Certain Regard section which aims to promote young film-makers.
The film sees Benson team up with Chastain more than a decade after they first met when he showed one of his early films.
He said: "She was my first fan and has believed in me for a long time, which I am extremely grateful for, because without that I'm not sure I'd have made this project."