No film critic with a heart wants to deliver the news that the Dardenne brothers have coughed up a dud. Jean-Pierre and Luc – who are among the exclusive club of two-time Palme d'Or winners – have been bossing the Cannes Film Festival since Rosetta triumphed here in 1999. The Unknown Girl is not quite a dud. If it had a young film-maker's name attached to it, we would be heralding his or her potential (to be the new Dardenne brothers, perhaps). But it lacks passion, plausibility and order.

Adèle Haenel is bizarrely deadened as Jenny Davin, a caring doctor working on the outskirts of Liège. As we join her, she is engaged in a war of wills with her inexplicably surly intern, Julien (Olivier Bonnaud). While they are scowling at one another, the buzzer goes and, thus distracted, they fail to answer the door.

It transpires that a young African woman was seeking sanctuary. The next day she is found dead and, stricken by guilt, Jenny sets out to identify her. The film becomes a sort of low-key, naturalistic detective story. It seems that the girl might have been a sex worker and might have a connection with one of Jenny’s patients.

Haenel's performance – a weird, sustained sulk, delivered at a reclining angle – is presumably aiming for the flatness of reality. But no amount of immobility can distract from the awkwardness of the storytelling. Jenny is the good doctor who can heal both body and soul with her endless sincerity. Jessica Fletcher had more angles to her personality in the (not wholly dissimilar) Murder, She Wrote.

The woman of the title never gets the fleshing out we've been promised. In just one regard, The Unknown Woman does improve on many Dardenne films: for once, nobody goes conveniently unconscious after a biff on the head.