New York’s downtown sweetheart Parker Posey is having a marquee summer. “Fay Grim” may be vaulting over the heads of many subscribers to Mark Cuban’s HDNet, the high-definition cable and satellite channel that produces its own theatrical content. But even people who don’t get Hal Hartley can still love the actress, who seems to occupy every frame of “Fay Grim,” deftly dancing through Mr. Hartley’s elliptical verbal rhythms.

“Broken English,” the debut by writer-director Zoe Cassavetes, is part two of the season’s Parker Posey double feature — like “Grim,” it’s also bankrolled by Mr. Cuban, and shot in identically washy hi-def video — and offers a more familiar perspective on a woman who wanders far from home in search of a missing lover. Ms. Posey inhabits her natural environment as Nora Wilder, who, to paraphrase John Cameron Mitchell’s coinage, is in her early-to-mid-late-30s, perpetually single, and bored stupid by her job as the hospitality director at one of those painfully hip hotels that cater to celebrity guests. Nora embodies a distinct Manhattan archetype that got played to death during six seasons of “Sex in the City”: the romantic neurotic career gal striving for love and self-realization in a sophisticated demimonde.

Yet Ms. Cassavetes has a more subtle touch with pen and camera, balancing a naturalistic feel with a pixilated comic pitch that plays a bit like a feminized Woody Allen. Nora’s particular midlife flux has her equally addicted to cigarettes and yoga, yo-yoing between drunken sex with two-timing Hollywood hunks and existential angst about her emotional stasis. Her best friend, Audrey (Drea de Matteo), offers a grass-is-greener contrast, lamenting her perfect, and perfectly sexless, marriage. Meanwhile, Nora’s mother (Gena Rowlands, the director’s real-life mother), sets her up on a misbegotten date with the son of a family friend.

One night, Nora meets an insistent French guy at a party she’s desperately trying to escape, and everything begins to change. Julien (Melvil Poupaud) is something of a stock character: the enigmatic Euro artiste, whose snake hips and Parisian inflections possess an exoticism more compelling than chocolate. What begins as a fling becomes more philosophically obsessive.

It’s in this middle stretch, where the comic pacing is suspended and Ms. Posey spends a fair amount of time simply sitting quietly in a bedroom or on a couch, that the film seems to get somewhere: inside Nora’s head, for sure, but also exposing a side of Ms. Posey that rarely gets much play onscreen. Normally, everyone is so attached to her dynamic flow (especially in those Christopher Guest comedies), that to see her occupy a frame in stonecold silence, the light at play over the finely chiseled architecture of her face, is a kind of revelation.

Ms. Cassavetes doesn’t linger here. Narrative requirements dispatch her heroines on a reckless quest to Paris, where Nora casts, yes, fate to the breeze and hopes to track down the DJ who loved her. Instead, she finds herself in a conversation over such affairs with a Delphic doyenne played by the French actress Bernadette Lafont (the bicycle-riding object of desire in Francois Truffaut’s inaugural 1957 short “Le Mistons”). The momentary life lesson tilts Nora’s journey toward the kind of spiritual analysis of Elizabeth Gilbert’s autobiographical ramble “Eat, Pray, Love” — now being adapted for the screen by Julia Roberts — and almost makes Euro Dude irrelevant.

As the thinking woman’s chick flick, “Broken English” ultimately suggests how much Saturday night at America’s cineplexes could be improved if Ms. Posey didn’t play the sidekick in fluff like “You’ve Got Mail” but pulled a single-white-female maneuver and stuffed Meg Ryan in the closet. Alas, Ms. Posey has shown better taste, but the thought sure is amusing.