The occasion was marked by a string of cultural events including free Paris exhibitions in their honor.
Piaf was 47 when she died in 1963, having gained worldwide fame with La Vie en Rose, which remains among the top 10 French-language songs ever sold.
Cocteau, an artist, filmmaker and designer as well as an acclaimed novelist, died at the age of 74.
His life is being celebrated with an exhibition at the Pompidou Centre, while Piaf is the subject of an anniversary display at the Paris town hall.
"She interpreted her life through her songs. People could identify with her in that way and she always sang of love," said Bernard Marchois, head of the Friends of Edith Piaf, who keeps 5,000 Piaf artifacts in his home.