Jean-Paul Belmondo defined French cool at the beginning of the New Wave in Jean-Luc Godard’s 1960 classic “Breathless.” Actor Alain Delon and director Jean-Pierre Melville very consciously redefined it in 1967’s “Le Samourai,” in which Delon played a killer for hire always adjusting his fedora so it was just so. The actor was compared to James Dean.

But it was the hotly charismatic Belmondo who was more like Dean, who had been given to emotional outbursts in his performances. Delon was not only cool, he could also be cold.

Back when Delon was just starting out, he encountered David O. Selznick, perhaps while Selznick was shooting 1957’s “A Farewell to Arms” in Italy, or perhaps at Cannes. The producer offered him a contract provided that the nascent actor learn English, but Delon demurred.

His rejection of Hollywood helps explain why it may be hard for Americans to appreciate the extent of Delon’s fame during the 1960s and ’70s not just in France but in regions as diverse as Japan, Communist China (where a 1975 version of “Zorro” starring Delon as the popular hero was one of the first Western movies exhibited in the country after the Cultural Revolution) and Latin America.

In his best movies, such as Melville’s “Le Samourai” and Joseph Losey’s “Mr. Klein,” Delon was almost zen-like in his underplaying of the role, which served to draw viewers in and watch every detail of his performance.

In “Le Samourai” Melville, who was obsessed with American gangster and noir films, meticulously follows Delon’s assassin Jef Costello as he creates an alibi, knocks off the owner of a nightclub, makes it through a police lineup, finds that those who hired him have betrayed him and is hunted by the police. The plot is far, far less important than the style of the movie, the style of Delon’s portrayal of the killer. It is considered a masterpiece.

Articulating the nature of Delon’s extraordinary appeal, as crystallized in “Le Samourai,” can be difficult. Film scholar David Thomson described him as “the enigmatic angel of French film, only 32 in 1967, and nearly feminine. Yet so earnest and immaculate as to be thought lethal or potent. He was also close by then to the real French underworld.” Thomson added: “Delon is not so much a good actor as an astonishing presence — no wonder he was so thrilled to realize that the thing Melville most required was his willingness to be photographed.”

Delon offered a rare warmer side in a supporting role in Visconti’s 1963 masterwork “The Leopard,” in which Burt Lancaster played a 19th century Sicilian prince (the actor’s voice was dubbed) trying to cope with revolution and what it will mean for his family and his social class. Delon played his dashing nephew, who joins the revolutionaries, then throws in with the king’s army; he had palpable chemistry in the film with the beautiful Claudia Cardinale.

In 1962 Delon starred with Monica Vitti in Antonioni’s “L’Eclisse,” the second entry in the director’s justly famous alienation trilogy. Delon was perfectly cast as a wheeler-dealer stockbroker who becomes involved with Vitti’s character but is unwilling and unable to satisfy her emotional needs.

In Joseph Losey’s brilliant “Mr. Klein” (1976) Delon gave a tightly controlled performance as a Catholic art dealer in occupied Paris who takes advantage as rich Jews with art collections are carted away —  but begins to have problems of his own as he is increasingly mistaken for an elusive Jew who is using his name for secret operations.

Delon starred with Charles Bronson, Toshiro Mifune, Ursula Andress and Capucine in the Terence Young-directed international production “Red Sun” (1971); the Western, shot in Spain, was not much liked in the U.S. but enjoyed success in Europe and Asia. (Delon, who developed an interest in Japan as a result of “Le Samourai,” long enjoyed a following in the country, where sunglasses branded with his name were a hit.)

Delon reunited with his “The Leopard” co-star Burt Lancaster in 1973 for the Michael Winner-directed thriller “Scorpio,” in which Delon played an assassin ordered to eliminate Lancaster’s weary spy, who wants out of the game.

Despite rejecting Hollywood, Delon did do three American films over the years: 1964 crime drama “Once a Thief” with Ann-Margret and Van Heflin, 1966 Western “Four for Texas” with Dean Martin, plus “Airport ’79: The Concorde,” in which he played the captain of the troubled plane.

Perhaps his 80th birthday is a good opportunity to discover the film of the enigmatic French superstar Alain Delon.