Fifty years ago, a failing songwriter sat down at his piano in his Paris flat and furiously bashed out the melody of a new song. He was, he remembers, "angry and depressed". He had signed the lease for a new apartment but could scarcely afford to buy furniture, or food, for his wife and two children.

A couple of weeks ago, Charles Dumont sat down behind the same piano in the same apartment and – at my request – played, beautifully, to the soaring conclusion of what he calls the "song that changed my life".

His "angry" song has become one of the best-known, and best-loved, pieces of popular music, and remains the signature tune, and the epitaph, of the most enduring of all French popular singers, Edith Piaf (1915-1963).

Although the song had no title when Dumont composed it, it was transformed by his co-writer and lyricist, Michel Vaucaire, into a paean to the human spirit and the restorative power of love. Its title became: 'Non, Je Ne Regrette Rien'.

Dumont went on to write many other successful songs, for 'The Little Sparrow' and for others. With Piaf's encouragement, he became a much-admired singer himself, in the French balladeer tradition. Now, to mark his 80th birthday, he has released a double album of classic French love songs.

Dumont is cheerfully indestructible and is touring France this year, and next, with other golden oldie French singers, performing for audiences of up to 7,000 people. His repertoire consists of romantic standards, including 'Non, Je Ne Regrette Rien'.

"People ask if I don't get sick and tired of that song," Dumont said. "Or if I have come to resent its success, because, 50 years later, it's still what I'm best remembered for.

"No. To me that would be the height of ingratitude. Why should I resent, or be bored with, 'Non, Je Ne Regrette Rien'? How many people can say they helped to create something legendary, something magical, something I hope will live forever?

"I was reborn with that song; it transformed my life. It has been my calling card all over the world. It changed me from a jobbing songwriter, a fabricator of songs, to someone who had the confidence, and the opportunity, to write what I wanted and what I felt."

Dumont retells the story of how he "sold" his song to Edith Piaf half a century ago. By appointment, he and Vaucaire apprehensively rang her doorbell at the Boulevard Lannes, close to the Bois de Boulogne.

Piaf, exhausted by drink, drugs, multiple love affairs and road accidents, had retired, at the age of 44. She was refusing all appeals to make a comeback. She despised Dumont, whom she dismissed, he says, "as a mechanical songwriter of no great talent, someone who wrote mediocre numbers for half a dozen singers".

Piaf's assistant told the two men, apologetically, that the appointment had been cancelled. She had tried, she said, to leave messages. "Madame" had changed her mind.

They were about to leave. ("I was very angry," recalled Dumont) when one of the most famous voices in the world spoke from a distant bedroom. Since they had come, The Voice growled, they might as well come in. She would dress at once.

An hour later, Edith Piaf shuffled into the room – tiny, imperious, short-tempered. "I'll hear only one song," Piaf said to the two men. "Just one".

"I went to the piano in a great fury," Dumont recalled. "I knew she was going to reject me again. I played, and sang 'Non, Je Ne Regrette Rien', very, very loudly. There was a silence. Then she said: 'Play that again'.

"When I finished, Piaf asked, rather rudely: 'Did you really write that song. You?' I shrugged and said 'yes'. She said: 'That song will conquer the world'."

And so it did. Piaf came out of retirement. She sang it on French television the following month. It was the centrepiece of her comeback gala performance at the Olympia music hall in Paris in December 1960. A record was released in January. More than 100,000 copies were sold in two days and more than a million by the end of the year.

Dumont proudly showed me a copy of the original artwork from the album in which the song later appeared. Piaf, brought up in deep poverty in the back streets of Paris, has scrawled a tribute across the back which reads: "To you Charles, to thank you for the marvellous songs that you gave me. They allowed me to keep the love of the public and gave me, on 29 December 1960 – the night of the Olympia concert – the most wonderful evening of my career."

Several of Dumont's other songs have become French classics: 'Ta Cigarette Après L'amour', 'Les Chansons d'Amour' and 'Les Amants', which he recorded in duet with Piaf.

"When you are a singer, people – especially women – look at you differently. They don't see the old man. They see the voice or, if you like, the soul. To be regarded that way, well, it rejuvenates you. It regenerates you."

'Chante L'Amour' by Charles Dumont is out now on Sony Music