Anna Karina, a luminous star of French New Wave cinema who worked closely with director Jean-Luc Godard, “the strange guy with the dark glasses” who became her first husband — and who seemed to channel their tumultuous romance in his early films — died Dec. 14 at a hospital in Paris. She was 79.

Her death was announced by the French culture minister, Franck Riester, and by her agent, Laurent Balandras, who said the cause was cancer.

With her alabaster face, dark bangs and piercing teal eyes, Ms. Karina was an internationally recognized emblem of the French New Wave, when directors such as Godard and François Truffaut used portable equipment and daring aesthetic choices to upend mainstream filmmaking.

A onetime model and cabaret singer, Ms. Karina also recorded hit songs by Serge Gainsbourg, wrote several novels, worked with celebrated filmmakers such as Jacques Rivette and Luchino Visconti, and directed her own movie, the countercultural romance “Living Together” (1973).

But she was best known for playing enchanting, headstrong young women in her seven features with Godard. A 2012 Sight & Sound magazine directors’ poll of the 100 greatest films of all time included two of their movies: “Vivre Sa Vie” (“My Life to Live,” 1962), in which she starred as a young Parisian who leaves her husband and son to become an actress (then a prostitute), and “Pierrot le Fou” (“Pierrot the Madman,” 1965), a twist on the gangster genre in which she goes on the run with her ex-boyfriend, played by Jean-Paul Belmondo.

Even as Ms. Karina’s characters flirted with tragedy, they were frequently dancing giddily across the big screen, gamboling through an apartment and jumping on a bed in “The Little Soldier” (1963), strutting and spinning through a pool hall in “Vivre Sa Vie” and performing a finger-snapping variation on the Madison line dance in “Band of Outsiders” (1964).

Ms. Karina was also adept at depicting their inner turmoil and anguish, and at times seemed to draw on torturous episodes from her own life — including several years in foster care as a child, her fraught relationship with Godard and a suicide attempt that briefly landed her in a mental institution. “There were a lot of ups and downs in my life,” she told the Guardian in 2016. “And the downs were, you know, very down. Very low.”

Born in Denmark, Ms. Karina hitchhiked to Paris in 1957 and began modeling after she was spotted at the cafe Les Deux Magots. She soon met Coco Chanel, who suggested she use a stage name that recalled Tolstoy’s novel “Anna Karenina,” and was offered a role in Godard’s feature-length debut, the New Wave milestone “Breathless” (1960).

The director had apparently seen her in an ad for Palmolive soap and wanted her to do a nude scene, which Ms. Karina rejected. But months later, she received a telegram from Godard, asking if she wanted to star in his next film. “I showed it to some of my friends, they said: ‘Godard! You have to see him!’ ” she recalled in a 2016 interview with the New York Times. “I thought, ‘The strange guy with the dark glasses?’ ”

Ms. Karina went on to star as a model in “The Little Soldier,” which was banned in France until 1963 because of its graphic depiction of the Algerian War. Because of the delay, she made her feature-length debut in Godard’s “A Woman Is a Woman” (1961), as an exotic dancer who tries to persuade her lover (Jean-Claude Brialy) to settle down.

Just 20 years old upon its release, she earned the best actress award at the Berlin International Film Festival and married Godard (a decade older) that same year. In interviews, she sometimes likened their relationship to George Bernard Shaw’s play “Pygmalion,” describing Godard as a kind of cinematic Henry Higgins.

Undoubtedly, the partnership benefited his own career as well. Ms. Karina energized many of the filmmaker’s subsequent movies, which made him an explosive — if sometimes confounding — staple of American art houses. “Watching a Godard film was often the cinematic equivalent to being thrown off a cliff,” film scholar Jeanine Basinger once wrote in the Times. “Made in U.S.A.” (1966), she noted, began with a shot of Ms. Karina “and an inexplicable subtitle: ‘Happiness, for instance …’ What? Not to mention where, when, who or why.”

In interviews, Ms. Karina recalled a passionate but difficult relationship with Godard. “I could never understand his behavior,” she told the Guardian. “He would say he was going out for cigarettes and then come back three weeks later. And at that time, as a woman, you didn’t have any checkbooks, you didn’t have any money. So he was off seeing Ingmar Bergman in Sweden or William Faulkner in America. And I was sitting around the apartment without any food.”

She said that she had a miscarriage and attempted suicide before Godard cast her in “Band of Outsiders,” a heist movie that “probably saved my life.” She also starred in his dystopian science-fiction film “Alphaville” (1965), opposite a secret agent played by American actor Eddie Constantine.

By then, the couple had already separated, finalizing their divorce in December 1964, according to Richard Brody’s biography of Godard, “Everything Is Cinema.” In “Alphaville,” her character struggles to say the words “I love you,” Brody noted. “Through an extraordinary filter of genre, it would be a film in which Godard was desperate for life to imitate art.”

In the years before her death, however, Ms. Karina said it had been decades since she saw Godard, whom she described as a recluse. “I think about him with love, no hate,” she told W magazine in 2016. “It was a great love story. We were together for seven and a half years. It’s something you don’t forget, people talk about it all the time. It’s the greatest thing in the world when you get a gift like that.”

Ms. Karina was born Hanne Karin Blarke Bayer in Solbjerg, a suburb on Denmark’s eastern coast, on Sept. 22, 1940. Her father left the family when she was a young girl, and her mother was reportedly a costume designer for theatrical productions.

After moving to France, Ms. Karina had a small role in Agnès Varda’s “Cleo From 5 to 7” (1962), appearing alongside Godard in a silent film-within-the-film. She also starred in Rivette’s “The Nun” (1966), based on an 18th-century Denis Diderot novel about a girl forced to enter a convent. Her character is tormented and sexually harassed, and the movie’s release was blocked by French authorities before it premiered at the Cannes Film Festival.

“Ms. Karina’s beauty, for which Godard once made movies that were also homages, is the perfect centerpiece for a film that looks cool and graceful but is passionately determined with the heart of a revolutionary,” wrote New York Times critic Vincent Canby. “It’s a lovely performance, one that never condescends to play on pathos but grows in strength with each new outrage.”

Her marriages to Pierre Fabre and Daniel Duval ended in divorce, and in 1982 she married Dennis Berry, an American actor and director who was previously married to “Breathless” star Jean Seberg. According to Britain’s Independent newspaper, they divorced in 1994 but resumed a relationship in recent years. Complete information on survivors was not immediately available.

Later in her career, Ms. Karina played Michael Caine’s spurned lover in “The Magus” (1968), based on a best-selling novel by John Fowles, and was featured in Visconti’s “The Stranger” (1967), George Cukor’s “Justine” (1969), Tony Richardson’s “Laughter in the Dark” (1969) and Rainer Werner Fassbinder’s “Chinese Roulette” (1976). But she remained forever tied to her work with Godard, somewhat to her surprise.

“We never thought the films would be so famous for so long,” she told the Times in 2016. “We were just happy to do things. It was more bohemian. We knew we were doing something we liked and it was not like everyone else. It was a happy world.”

Correction: An earlier version of this obituary incorrectly described the plot of “Vivre Sa Vie.” Ms. Karina starred as a young Parisian who leaves her husband and son to become an actress, and only later works as a prostitute. This story has been updated.