Had Sidney Falco been played by Woody Allen, the driven press agent of “Sweet Smell of Success” might have grown up to become Norman Oppenheimer, the character Richard Gere plays in Joseph Cedar’s satire-spiced drama about a small-time New York operator who almost accidentally becomes a power player in Israeli politics and finds the role a very uncomfortable one. “Norman: The Moderate Rise and Tragic Fall of a New York Fixer” is a strange film, alternately credible and ludicrous, compelling and dull, darkly funny and gloomily depressing, though bolstered by a star turn that’s basically a stunt but is still an enjoyable one.

When we first meet Norman, he’s pressing his nephew Philip (Michael Sheen), a Wall Street lawyer, for the names of contacts he could approach to put together deals. And in truth we never get to know much more about him than that. There’s no indication of where he lives, or of any other friends apart from Philip and his rabbi, Blumenthal (Steve Buscemi), whose attitude toward him is one of resigned tolerance. Oppenheimer seems to spend all of his time trudging the streets looking for opportunities, or accosting targets like Bill Kavish (Dan Stevens), an aide to big-time investor Jo Wilf (Harris Yulin), while the poor guy is out jogging, to try to set up a meeting with his boss.

When that fails, he takes an interest in Micha Eshel (Lior Ashkenazi), a deputy minister in the Israeli government, whom he sees at a Jewish-American conference. Literally trailing him as the fellow walks back to his hotel, Norman impulsively buys Eshel a pair of costly shoes the guy has admired in a store window—a ploy to entice him to meet with another important investor named Taub (Josh Charles).

That doesn’t work out either—in fact it ends in Norman’s humiliation—but three years later Eshel has become Prime Minister of Israel, and he recognizes Oppenheimer in the crowd at a public gathering of power players when he visits the U.S. Suddenly Norman finds himself the focus of attention from important people who haven’t the foggiest idea of who he is. No wonder he has a tendency to blab about his connection to Eshel to anyone within earshot, including an ambitious Israeli woman named Alex (Charlotte Gainsbourg) he shares an airline flight with. And that tendency continues, despite the fact that Eshel’s handlers cut off all contact between the two.

Yet when the Prime Minister, despite great resistance, becomes an advocate for peace, he comes under attack from his opponents for alleged financial improprieties with an unidentified American businessman and charged with taking bribes. Oppenheimer wants to be of help to him, but is stymied by the PM’s handlers. What he doesn’t know is that he’s the unidentified businessman. Meanwhile he’s caught up in two related matters. He’s trying to rescue Blumenthal’s synagogue from foreclosure by finding a donor to cover a multi-million dollar bill, and one possibility is Wilf, who’s looking to secure an interview with an Israeli official that Norman promises to arrange. He also reaches out to Philip, a Harvard grad, to arrange some help for Eshel, who’s trying to get his son into the school despite the boy’s indifferent academic record, and in turn hopes to get Blumenthal to officiate at his nephew’s hoped-for marriage to a Korean girl. All this is further complicated by a mysterious man (Hank Azaria) who begins following Oppenheimer, and by the fact that Alex turns out to be the lead investigator of the charges against Eshel. How all this can be sorted out forms the crux of the film’s last act.

There’s a cynical undertone to Cedar’s screenplay, of course: everyone is venal in his own way, willing to exchange favors for favors—Norman’s stock-in-trade, though in the end it’s clear that virtually everybody else is better at it than he is—he’s the real naïf, despite all his bluster. (The plot thread about the opposition to Eshel in the Israeli Knesset is a particularly thorny element, given that accusations of bribery have in fact led to the fall and prosecution of Israeli prime ministers in the past.)

Whatever qualms one might harbor about that, however, the central weakness of “Norman” has to do with the title character himself. Gere, vacillating between jittery fluster and somber reflection, hits all the right notes in the role; he makes Oppenheim a pathetic figure desperate to be of service. But the “why” behind his desperation is never even addressed, let alone answered. He remains a sketch—in Gere’s hands a vivid sketch, to be sure—but never a full portrait. That leaves an aching gap at the center of the story.

Still, it’s difficult one’s eyes off Gere, and the supporting cast mostly contribute colorful turns, especially Ashkenazi, Sheen, Buscemi, Azaria and Yulin. The only serious disappointment is Gainsbourg, not because she isn’t perfectly fine but because her role is terribly underwritten. (Stevens, incidentally, is becoming a chameleon—he’s practically unrecognizable here.) The picture is technically adequate, though Yaron Scharf’s cinematography is mostly notable for capturing the crisply uncomfortable ambience of Manhattan in the winter.

In the end the “Dr. Strangelove”-style subtitle of “Norman” is strangely prescient. This is a movie that’s artistically up and down, coming in roughly at the middle of the spectrum between fascinating and tedious. Gere’s committed performance makes it lean toward the former, but it still remains a hit-and-miss affair.