The French filmmaker Julie Delpy is still best known as an actor, but she’s been building a varied and impressive filmography as a feature writer and a director since the early part of the century. Her new picture, “My Zoe,” in which she also stars, is an unusually compelling domestic drama with sharp ears, a sharp eye, and up to a point, sharp teeth.

Delpy plays Isabelle, a geneticist living in Berlin with her young and adorable daughter Zoe. Her ex-husband, James (Richard Armitage), seems a perpetual and arbitrary thorn in her side, constantly needling her about visitation days and the competence of babysitters. The bickering doesn’t stop when disaster strikes. While their daughter has surgery to relieve the pressure on her brain caused by an aneurysm, Isabelle and James argue about their married sex life.

Sounds like something to be appalled by. But Delpy writes these characters with such depth, and stages their interactions with such sensitivity, that you understand them without necessarily approving of them.

The movie takes a likely unexpected turn from the conventional bad marriage story. Isabelle travels to Russia, appealing to a controversial medical researcher, Thomas Fischer (the frequent Delpy collaborator Daniel Bruhl), for a radical solution to a family tragedy.

For nonspoiler purposes, let’s call that solution “the shiny object” — a project of dubious ethics, and little probability of succeeding, that nevertheless proves irresistible to all who contemplate it. As it happens, it proves irresistible to filmmaker Delpy as well. It’s in her embrace of it that the movie, so tart and assured up to a certain point, goes wrong. But Delpy is a sufficiently assertive cinematic voice that she’s well worth arguing — and maybe ultimately disagreeing — with.

My Zoe
Rated R for language and themes. Running time: Running time: 1 hour 40 minutes. In theaters. Please consult the guidelines outlined by the Centers for Disease Control and Prevention before watching movies inside theaters.