The music of the composer, singer, arranger, conductor, jazz musician and producer Michel Legrand went on glowing long after many of the 250-odd films he had written soundtracks for had fallen by the wayside.

Legrand, who has died aged 86, made deadpan reference to that phenomenon when he played at Ronnie Scott’s club in London in 2011 – announcing that it was his ambition to meet “one of the 19 people who ever saw The Happy Ending”, the 1969 Hollywood film for which he wrote his classic love song What Are You Doing the Rest of Your Life?

But if some of the film vehicles for Legrand’s artistry were outlasted by his music, several became famous, including The Umbrellas of Cherbourg (1964) and Norman Jewison’s The Thomas Crown Affair (1968), with Noel Harrison singing The Windmills of Your Mind, which won Legrand’s first Oscar, for best film theme song, in 1969. Another Oscar followed for The Summer of ’42 two years later – this time for best film music. Its theme, The Summer Knows, was recorded later that year by Barbra Streisand, whose 1983 film, Yentl, won him his third Oscar, again for best music.

The famous Legrand Jazz album. Photograph: Sabine Weiss/Columbia Records

Legrand’s songwriting skills flowered in the early 1950s through intimate acquaintance with the modern chanson movement in Paris, at first as a gifted piano accompanist. After the second world war, the US was nostalgic for French culture, and when Columbia Records commissioned an English-language album of chanson classics, the young Legrand was hired to steer it – and found himself with an 8m-selling hit.

By his mid-20s, Legrand was able to call the shots as a composer and arranger on both sides of the Atlantic. In 1958, he even had more than sufficient clout to hire Miles Davis, John Coltrane and Bill Evans – three of the hippest and most acclaimed young jazz musicians of the decade – to play sidemen’s roles on his Legrand Jazz session.

Michel was born in the Paris suburb of Bécon-les-Bruyères into a family with strong musical connections. His father, Raymond Legrand, was a composer, conductor and former pupil of Gabriel Fauré, and in his later years would go on to collaborate with Edith Piaf and Maurice Chevalier. His maternal uncle on his mother Marcelle’s side was the dance-band saxophonist and bandleader Jacques Hélian.

But Raymond left home when Michel was three, and his mother Marcelle (nee Ter-Mikaëlian), struggled to provide for the boy and his older sister, Christiane. He found a consoling friend in the flat’s battered piano and it quickly emerged that he had a gift. Christiane also played the instrument, and she was similarly destined for a successful career in music, as a jazz singer.

Michel became obsessed with the music and life of Franz Schubert, and – with Nadia Boulanger among his teachers – won a raft of prizes on a variety of instruments at the Paris Conservatoire, which he began attending as a 10-year-old in 1942. But a 1947 Paris concert by the bebop trumpeter Dizzy Gillespie and his big band thrilled him with the sound of jazz.

By the time he left the conservatoire in 1949 he was a budding jazz pianist with a profound knowledge of musical theory and a working knowledge of many instruments. His resourcefulness quickly found him work with chanson stars including Juliette Gréco and Zizi Jeanmaire, and in 1954 the international popularity of chanson brought his international breakthrough.

Michel Legrand playing at the Royal Albert Hall, London, in the mid-1970s. Photograph: David Redfern/Redferns

Columbia-EMI wanted an English-language version of those evocative Parisian songs, and none of the big-name American arrangers was interested. Through a contact at the record company, the unknown Legrand was commissioned to produce it – for $200 and no royalties. The result was the bestseling album I Love Paris,. Chevalier then hired Legrand as his musical director and the resulting US tours enhanced the newcomer’s stature.

Legrand began a solo career, with the easy-listening but sophisticated jazz albums Holiday in Rome (1955), Michel Legrand Plays Cole Porter (1957) and Legrand in Rio (1958). He also worked with the French Caribbean singer Henri Salvador, who, under the alias of Henri Cording, made some of the first French forays into rock’n’roll, with Legrand furnishing the music and the surrealist novelist, poet and jazz critic Boris Vian the lyrics. In 1958, he returned to New York to make his celebrated Legrand Jazz album – with Ben Webster joining Coltrane, Evans and Davis in the lineup.

Legrand later admitted to being anxious about Davis’s involvement. The trumpeter rarely played sessions other than his own and made a diva’s point of arriving 15 minutes late, checking out the music from the studio doorway and promptly leaving if he did not like the sound of it. But, according to Legrand, the usually taciturn Davis not only participated, but even asked the young bandleader if he had liked his contribution.

By this point, Legrand was developing a parallel career as a film composer. He scored Henri Verneuil’s 1955 crime passionel movie Les Amants du Tage (The Lovers of Lisbon), and became a significant collaborator with the new wave directors Jean-Luc Godard, Agnès Varda and François Reichenbach. He also composed for Jacques Demy, most notably on the innovative Les Parapluies de Cherbourg (The Umbrellas of Cherbourg) – a reappraisal of the film musical, combining a realist perspective with a narrative in which songs replaced dialogue.

The movie’s theme song Je Ne Pourrai Jamais Vivre Sans Toi was covered – in English as I Will Wait for You – by stars including Frank Sinatra, Tony Bennett and Liza Minnelli. Legrand, Demy and the film’s lead, Catherine Deneuve, collaborated on the Hollywood homage Les Demoiselles de Rochefort (The Young Girls of Rochefort, 1967), with Gene Kelly. Legrand also wrote for Gilles Grangier and Yves Allégret, and for Joseph Losey – most notably in 1971 on the Palme d’Or winner The Go-Between.

Through close relationships with the jazz-enthusiastic chanson singer Claude Nougaro and the Belgian singer-songwriter Jacques Brel, Legrand not only began to develop a personal repertoire of original songs, but to consider performing them himself. He collaborated on the lyrics with other writers including Eddy Marnay and Jean Dréjac, and worked on the occasional forays into songwriting by the novelist Françoise Sagan.

In 1968, Legrand moved to Los Angeles, during which time he composed the award-winning scores to The Thomas Crown Affair and then, two years later, Summer of ’42. Legrand later said that Jewison cut the highly charged seven-and-a-half-minute chess game scene between Steve McQueen and Faye Dunaway in The Thomas Crown Affair to fit the music, which begins with a solo harp and ends with a big band playing a jazz waltz.

As well as the Oscars, between 1971 and 1975 Legrand won five Grammy awards, and in this period was on his way to becoming one of the US’s most popular Frenchmen. A sharp and witty raconteur, he appeared on television chatshows, and for relaxation worked at Shelly’s Manne Hole club in Los Angeles with the great double bassist Ray Brown. In the next decade, he composed for Clint Eastwood and Orson Welles, for Streisand’s Yentl, and the James Bond film Never Say Never Again (1983).

During this time Legrand also played a lot of jazz, making three albums with a regular trio featuring the bassist Marc-Michel Le Bévillon and the drummer André Ceccarelli, and bringing together the celebrated American saxophonists Phil Woods and Zoot Sims to join him in a septet to make the 1982 album After the Rain. He released a solo vocal album, and staged his own oratorio, inspired by the Universal Declaration of Human Rights, as part of the celebrations for the bicentenary of the French Revolution, in 1989.

Legrand’s search for new challenges found one that even he could not pull off when he directed the unsuccessful semi-autobiographical film Cinq Jours en Juin (1989), but leading a big band in the next decade found him on more secure ground – he toured widely, and accompanied Ray Charles, Diana Ross and Björk with it. Legrand composed for Jean Guidoni’s 1995 album Vertigo and participated in an award-winning show at the Casino de Paris with Guidoni the following year.

In 1997, with the playwright Didier Van Cauwelaert, he worked on Le Passe Muraille, a quirky musical adapted from a 1943 Marcel Aymé short story about an unassuming clerk who can walk through walls. The show went to Broadway as Amour five years later, and its lead singer Melissa Errico became an important muse for Legrand. They worked together for six years on the album Legrand Affair (2011).

In his later years, Legrand remained ready for surprises, even if the world was beginning to treat him as a grand old man. Stars queued up to perform his hits in a celebration at the Louvre in 2000; and the French government made him an officier de la Légion d’honneur in 2003.

When his friend Nougaro died in 2004, he recorded Legrand Nougaro, where the composer and a bespoke jazz band accompanied tapes of his friend’s voice in new performances of the Toulouse singer’s songs – including the previously unheard Mon Dernier Concert.

In 2009 Legrand came to Britain with a repertoire combining his biggest hits and a selection of jazz favourites, and a lineup including his longterm partner, the harpist Catherine Michel and the singer Alison Moyet. The following year, he conducted the Moscow Virtuosi chamber group in Russia, for the two-CD set The Music of Michel Legrand. And for his 80th birthday Christmas album the following year – Noël! Noël!! Noël!!! – Legrand was joined by Rufus Wainwright, Jamie Cullum and Iggy Pop.

“When I hit 80,” he said, “I knew that the last chapter of my work would be classical. So I wrote a piano concerto that I recorded myself, a cello concerto, a harp concerto, some sonatas. I wrote a huge ballet. I’m very proud of that. It’s a good final chapter.”

Last September, Legrand conducted orchestral arrangements of music from his soundtracks with the Royal Philharmonic Orchestra, against projections of the scenes they originally accompanied, at the Royal Festival Hall, in London.

He lived his last years as he had lived his earliest ones as a precocious music student in Paris – guided, as he said, by the “ambition … to live completely surrounded by music. My dream is not to miss out anything. That’s why I’ve never settled on one musical discipline. I love playing, conducting, singing and writing, and in all styles. So I turn my hand to everything – not just a bit of everything. Quite the opposite, I do all these activities at once, seriously, sincerely and with deep commitment.”

Legrand had three marriages. The first, to Christine Bouchard, a model, and second, to the actor and producer Isabelle Rondon, ended in divorce. In 2014, he married the actor Macha Méril.

He is survived by Macha and his four children, Dominique, Hervé, Benjamin and Eugénie.

• Michel Jean Legrand, composer and musician, born 24 February 1932; died 26 January 2019