Isabelle Huppert as sweet surrogate mom turned psycho stalker in ‘Greta’

If you see a suspicious package or activity on the train or the platform, please tell a police officer or an M.T.A. employee. What New York subway rider doesn’t know that?

A young woman named Frances - a recent transplant from Boston, as if that’s an excuse - who finds an expensive-looking handbag on the Lexington Avenue local and pays dearly for ignoring mass transit protocol. “Greta,” the movie about what happens to Frankie (as she’s called), can stand as a cautionary tale for straphangers. If you see something, say something.

Having seen it, I will say that “Greta,” directed by the always-estimable Neil Jordan (“The Crying Game,” “Michael Collins,” “The End of the Affair”), is a mixed bag, a skillfully executed psychological thriller with not quite enough in the way of psychology or thrills to be as disturbing or diverting as it should be. And maybe not enough Isabelle Huppert, either, though she is the major and almost sufficient reason to bother with the film in the first place.

Huppert plays Greta, the owner of that purse and a bunch more like it, accessories that she uses to lure young women like Frankie to her house in Brooklyn. Frankie (Chloë Grace Moretz), whose mother has recently died and who is semi-estranged from her father (Colm Feore), finds in the older woman a mirror for her own loneliness. Greta has lost a husband and a dog, and misses her daughter, who she says is off in Paris studying music.

Greta’s empty nest is filled with Chopin and Liszt and strange noises from behind the piano, and she and Frankie strike up what seems to be a warm intergenerational friendship. Frankie’s roommate, Erica (Maika Monroe, supplying a superfluous but satisfying jolt of bratty energy), thinks it’s a little weird, and of course she turns out to be right. The lady has a cupboard full of identical handbags! Then she goes full stalker, flooding Frankie’s phone with texts and voice mail messages and showing up at the restaurant where Frankie works.

Frankie is probably too young to have seen “Fatal Attraction,” “Single White Female” or the other madwoman-in-the-city movies of the ’80s and ’90s. “Greta” updates the genre (people have smartphones now) without improving on it much, though the maniac-mommy twist is an interesting wrinkle, adding a sinister fairy-tale element to the modern setting. (It’s hard to hear the title without thinking of Hansel and Gretel, and Greta is distinctly witchy.) But the plot moves a little too quickly from intriguing ambiguity to straight-up terror, without giving Moretz and Huppert enough time to explore the kinks in the characters’ relationship or the temperamental contrast between them.

Moretz is soft-featured and forthright, her face a blunt register of Frankie’s feelings. Huppert is all angles and shadows, and Greta is a mystery wrapped in an enigma bundled up in a neatly tied package of pure crazy. The scrip makes a small effort to explain Greta’s mania, or at least to fill in her background - a hapless detective played by Stephen Rea is deployed for that purpose - but understanding what makes her tick is not even remotely the point of the movie.

The point, and the fun, is the wild mischief of Huppert’s performance, which grows lighter and more joyful as Greta’s behavior slides from menacing to murderous. Jordan contrives to make Huppert’s mere presence in the frame almost absurdly frightening, and Huppert compounds the fright with elegant comedy, so that while the movie is impossible to take seriously, it’s also hard to resist, like an unattended bag on the subway that’s just begging you to look inside.