If Louise, the main character of Dylan Kidd’s new movie P.S., were played by a less likeable actor than Laura Linney, we mightn’t much care about her. Linney is not exactly “beautiful”, whatever that means, and the everyday sweetness of her laugh will always close her out of the empyrean inhabited by high-toned, unpredictably savage performers like, say, Isabelle Huppert. But she has this special quality, one hardly knows what to call it, of repaying attention. It is always gratifying to watch her subtly endow the simplest-seeming character with what used to be called an inner life.

So it’s worth putting up with what’s clunky, ill-handled and confusing about this movie – Louise’s irritating best friend and erstwhile high-school rival Missy (Marcia Gay Harden), her mother (Lois Smith) with her crocheted rugs and heavily symbolic suburban bulb-planting, and her ex-addict brother (Paul Rudd) who is dragged in by the coat-tails to offer sensible remarks about the meaning of life – just to see what Linney, this time, has in store.

Louise has a pleasantly powerful job in the admissions office at Columbia University’s School of Fine Arts. She’s in her late thirties, good-looking and intelligent, but her nervy, impatient way of dotting skin cream onto her face at the bathroom mirror hints that something is wrong with her life: a light in her has gone out.

Her former husband Peter (Gabriel Byrne), a lugubrious older academic whose student she once was and whose infidelity broke up their childless marriage, is hanging around her more than any ex should. Shake him off, we think crossly; but they have to eat their sandwiches together, because the movie hasn’t quite scrambled across the bridge from the novel it’s based on, and a lot of vital back-story is transmitted in their creaky lunchtime conversations.

One day at her desk at the admissions office Louise opens an application bearing the same name – F. Scott Feinstadt – as that of the young painter who broke her heart when she was 19. He not only dumped her for her sex-bomb friend but made the damage forever irreparable by getting himself killed in a car crash. Shaken by the sight of the name, Louise breaks protocol, phones the bewildered young applicant, and in a trembling voice summons him for an interview.

When F. Scott Feinstadt (Topher Grace) steps into her office, a flood of life enters with him. Another director might have tried for greater complexity by making the young man plain, even nerdish. But this is a romantic comedy, a variation on the older woman/younger man theme with an undertone, God help us, of sexual harassment – so the kid has to be gorgeous, and he is. Wow – those clear eyes, that creamy skin, that open-faced niceness!

Louise, wearing for the occasion a dress that shows an uncharacteristic amount of breast, takes one look and basically, well, throws herself at him. F. Scott Feinstadt hasn’t a clue what’s going on, but he’s game, and within the hour she’s on his lap in her apartment and they’re making love on the sofa under the original F. Scott Feinstadt’s rather muddy blue abstract, which we already know is supposed to be a portrait of Louise entitled “Mother and Child”.

This urgently erotic scene is shot with great delicacy. It zings with excitement, gasping pleasure and even a sort of genial wit. They have hardly got their breath back and re-arranged their garments before he shyly asks if “this” will hurt his chances of getting into the course. Can she separate business and pleasure? Also, may he use the phone? His mother will be waiting to hear how the interview went.

Topher Grace’s lovely F. Scott is the psychological and emotional core of the film, its reason to exist. Whenever he’s on screen, the world lights up; his absences from it feel interminable. In a cafe after their first encounter, Louise orders a dish of pasta and hoes into it with the eagerness of someone whose appetites have just been revived. F. Scott sits with his arm round the back of her chair and gazes down at her, while she eats, with a delighted fondness that is somehow hilarious. The next time he arrives at her apartment he sees she’s been crying. Instead of recoiling in panic, he takes her in his arms and asks with concern: “Is this about me?”

“No. My ex-husband just told me some things.”

“I didn’t know you were married!” says the student.

“I’m 39,” she replies tartly. “We met yesterday.”

What Peter has belatedly told her – and what he wants her forgiveness for – makes us shift in our seats with embarrassment. It seems to belong in some other movie, and so does Gabriel Byrne, glooming away in his abyss of guilt, while all we want is for F. Scott to bounce through the door again in his floppy check shirt, to freshen the morbid adult air with his youth and candour. “OK. Some guy broke your heart,” he says to Louise, when she finally tells him about his namesake. “But you know what? It happens to everybody. It’s called high school.”

I probably would have already forgotten this flawed, clumsy, yet oddly cheering little movie if it weren’t for an affecting scene, in her bedroom, between F. Scott and Louise. The chemistry between Grace and Linney goes much deeper than the frisson that makes a sex scene convincing. They are two really good actors at work, communing on a level that must have surprised them as much as it does the audience.

In the dim room she challenges him to enter an imagined realm more psychological than sexual, to enact a bitterly playful version of her lost past that wipes the smile of simple niceness off his face. This is where the age difference really bites, but he has more nerve and more resources than he knows. Something real happens between them, and this is what makes the movie memorable – this, and the stream of delicate expressions that flows across Topher Grace’s face, late in the piece, when he opens the envelope Louise has given him and finds in it the shape of his immediate future, and her estimate of his worth as an artist and a man.