There are two main reasons to restore and revive a film: one is artistic merit; the other is historical significance. The French director Louis Malle’s 1958 film “Elevator to the Gallows,” opening at Film Forum today, in a new restoration, meets the second standard but not the first. The direction isn’t particularly inventive, the script isn’t very substantial, and even the excellent cast, headed by Jeanne Moreau and Maurice Ronet, isn’t given much to do. Its historical significance, however, is that it looked, for a moment, like what a New Wave film might be—and even offered crucial elements that burst into full flower when the real thing came along.

Written by Malle and Roger Nimier (based on a novel by Noël Calef), “Elevator” is a melancholy melodrama that’s centered on the office of an arms dealer, Simon Carala (Jean Wall). His wife, Florence (Moreau), and his right-hand man, Julien Tavernier (Ronet), are in love, and they plot a crime that goes ludicrously awry when Julien gets stuck in an elevator. A second crime story, involving a young tough guy named Louis (Georges Poujouly) and a shopgirl (Yori Bertin) who are incidentally connected to Julien, soon follows. The elevator mishap, the center of the movie, is absurd and turns the film into an instant and derisive comedy. Yet Malle directs it, and the whole film, unrelievedly earnestly, adding a sneer of world-weary indifference that plays like a pose—but that pose has an intellectual foundation. Malle stuffs the movie with sociopolitical markers, starting with war talk. Julien is well known as a former paratrooper in France’s wars in Vietnam and Algeria (the latter, ongoing when the film was made) and as a former member of the Foreign Legion. Talk of recent wars and their fallout crops up throughout the film. When Louis, the petty hoodlum, meets a fatuous middle-aged German who complains about the lack of champagne during the Occupation—the postwar occupation of Germany by the Allies—Louis even talks like a case study, responding that he himself doesn’t at all care about champagne: “My generation has other things on its mind: four years of Occupation, Indochina, Algeria.”

The story’s facile connections between France’s sordid politics and its sordid crimes, however, are less convincing than its other, nondramatic documentary elements. What Malle does with the creaky story is far better than the story itself: he films it on location in and around Paris. His cinematographer, Henri Decaë—who had already done striking work with Jean-Pierre Melville and would go on to shoot the first features of Claude Chabrol (including “À Double Tour”) and François Truffaut (“The 400 Blows”)—lends the streets and buildings of Paris and its suburbs a hard, gray cinematic life. The best performance, by far, is that of Moreau, because Malle includes extended scenes of her essentially doing nothing—wandering the streets of Paris at night and contemplating her troubles—and he had the inspiration to notice that Moreau doing almost nothing is an absorbing spectacle in itself.

“Elevator to the Gallows” isn’t a New Wave film, but it is significant for its proto-New-Wavishness, its efforts toward originality and modernity. More specifically, such incidental elements as a big American car and the theft of that big American car, the accidental discovery of a handgun in the glove compartment of that car, the thief of that car committing a murder with that gun and going on the run in Paris with his young and innocent girlfriend, the young woman’s cramped one-room apartment, the record player and art poster in the apartment, the classical music playing on the record player as she and her boyfriend go to bed, the fugitive who sees his picture on the front page of a newspaper—all of these details should seem familiar, because they all turn up in Jean-Luc Godard’s “Breathless,” which came out two years later.

Although “Breathless,” shot in 1959, is based on a widely reported true-crime story that took place in France in 1952—and on a story that he and François Truffaut developed in 1956, long before Malle’s film was made—it was made in the light of a local cinematic renewal of which Malle (who was only twenty-six when he completed the film) was a crucial agent. Godard was working as a critic at the time of its release, but he never reviewed “Elevator to the Gallows,” and didn’t speak of it in interviews at the time of his first film’s release. But he had to have seen it.

Even the jazz-based soundtrack of “Breathless,” composed by the notable pianist Martial Solal, flows from the same stream. If there is a third reason to restore a film, it’s for the artistic merit of its ancillary elements, and that’s where “Elevator to the Gallows” stands out. Its score, composed by Miles Davis and performed (in Paris) by Davis and his local pickup quintet (featuring three good French musicians and the great American expatriate drummer Kenny Clarke), is worth hearing entirely on its own. It’s better than the film itself, by far, and there are better ways to hear it than in the movie—namely, by listening to a CD that features the entire studio sessions from which the score was edited.

Solal’s score for “Breathless” is memorable for its catchy themes and distinctive tone, but Solal noted that Godard took his half hour of music and reduced it mainly to two recurring five-note leitmotifs. Malle did no such thing with Davis’s music, featuring eight of the trumpeter’s extended improvisations, which run on the soundtrack for two or three minutes at a stretch. In “Milestones,” a magisterial two-volume biography of Davis, Jack Chambers puts the “Elevator to the Gallows” soundtrack recording into historical perspective, citing the use of jazz scores as a trend in the mid-to-late nineteen-fifties. “The use of jazz and jazz-derived soundtracks became so predominant,” he wrote, “that jazz came to seem like the natural backdrop for high-speed chases, mass mayhem, and cold-blooded murder, because the films for which jazz players were enlisted were uniformly violent.” Given that jazz is essentially an African-American art form and the movies were made by white producers, the association is both all the more unpleasant and all the more unfortunately explicable.

There’s nothing violent or sinister in Davis’s music for “Elevator to the Gallows,” which, despite its occasional origins, is both an enduringly mighty set of performances and a document of a hinge moment in Davis’s career, as the French release of the soundtrack sessions—featuring the entire batch of recordings in their original order and form—makes clear. For that matter, the texts in its booklet are themselves more deeply evocative of the spirit of Davis’s music than is the entire movie. They include a 1988 interview with the impresario Marcel Romano, who had arranged Davis’s European tour: