Achieving significant chart success across France, Belgium, the Netherlands, and Canada, "Non, Je Ne Regrette Rien" also gained recognition globally, notably quoted by former British Chancellor Norman Lamont in 1993, illustrating its cultural impact. In a retrospective interview, Dumont conveyed his initial hesitance in presenting the song to Piaf, having faced rejection from her previously. However, with encouragement from lyricist Michel Vaucaire, he returned to Piaf's door, leading to a prolific partnership that spawned over 30 songs until Piaf's passing in 1963.

Dumont's musical reach extended beyond Piaf, penning works for luminaries like Jacques Brel, Juliette Gréco, and Barbra Streisand. He transitioned to a successful solo career in the 1970s, leaving behind an enduring mark on French and international music. Edith Piaf, known for her powerful ballads and rough beginnings in the streets of Paris, remains a celebrated figure in music history, with Dumont's compositions forever part of her legacy.