Perhaps it’s appropriate that the director of “The Immigrant” has achieved more fame overseas than on his own shores.

In France, James Gray is practically a household name. Though he hails from New York — Queens to be exact — four of his five films have premiered at the Cannes Festival, and he has been nominated twice for the foreign film prize at France’s Cesar Awards. Even casual French film buffs know his resume. So why is Gray a virtual unknown to most Americans?

The director himself is a bit perplexed by his outsized international reputation, which began when his debut feature, the Brighton Beach-set crime thriller “Little Odessa,” was invited to premiere at the Venice Film Festival in 1994, when Gray was 25. Six years after that came “The Yards,” about a man caught in the middle of a turf war in a Queens railroad yard, followed by crime drama “We Own the Night” and stormy romance “Two Lovers,” a Dostoevskian meller which has started to transform his perception among U.S. auds.

“At the risk of sounding self-serving, if you had to choose a group of people you would hope would respond to your films, you’d choose the French. Throughout history, they have always been ahead of the curve in praising American directors,” says Gray, who accepts the fact that appreciation for his films in the States seems to come after their theatrical runs. But that also brings a certain disappointment for the director, a classic-film aficionado who considers “The Immigrant” his most personal project yet. The 1920s-set historical drama, which stars Marion Cotillard as a Polish woman who goes astray after passing through Ellis Island, was inspired by stories his family members shared about their early days in the U.S.

Just as Martin Scorsese has Leonardo DiCaprio, and Tim Burton has Johnny Depp, Gray has collaborated with Joaquin Phoenix on every film since “The Yards.” In “The Immigrant,” Gray based the tragic figure Phoenix portrays on Max Hoch-stim, a real-life pimp who used to frequent his great-grandfather’s Lower East Side restaurant, Hurwitz’s, often accompanied by an entourage of women.

Though the film was completed in time for 2012’s Toronto fest, U.S. distrib the Weinstein Co. insisted on holding it until Cannes, with Harvey Weinstein hoping he might convince the director to change the ending. Now, nearly an entire year later — after the film has already been released on DVD in France — Weinstein will open “The Immigrant” on four screens May 16.

That’s a tall order for a movie that makes minimal concessions to passing Hollywood fads. Whereas Gray’s past films have often been compared with classic ’70s cinema, “The Immigrant” takes an even more old-fashioned approach, embracing an almost operatic form of storytelling — a throwback that isn’t exactly all the rage with younger, superhero-obsessed, opening-weekend crowds.

“To me, to do something winking, post-modern and glib is not really radical in the context of cinema, because cinema has always been a popular-culture medium,” Gray says, instead casting his lot with a silent film director known for the melodramatic. “I tried to make something that had no wall between us and the characters, that was so filled with sympathy and empathy for the characters, to out-Frank-Borzage Frank Borzage.”

Making an elaborate New York period piece on a budget of less than $13 million took considerable ambition, but it’s nothing compared with Gray’s next project, an adaptation of David Grann’s “The Lost City of Z,” about an Amazon explorer who disappeared while searching for a missing civilization — the sort of loony, “Fitzcarraldo”-like project that could make Gray famous outside of France … or infamous.

“I wrote Francis Ford Coppola and told him we were shooting in the jungle, asking for advice, and he wrote back two words: ‘Don’t go.’ ”