Milord is a direct address, a term of respect used for a nobleman or a distinguished gentleman, similar to "My Lord" in English. It's not a common everyday word, making it quite distinctive.
In the context of the song, Piaf's character, a working-class woman, uses this formal address to a wealthy, heartbroken Englishman she encounters. The repeated use of Milord throughout the song highlights the class difference and her affectionate, yet somewhat deferential, attempt to comfort him, making it central to the song's narrative and charm.
"Milord" is Édith Piaf singing as a dockside girl in a French port town, calling out to an English gentleman she's noticed passing by.
She admits she's nobody to him, just a shadow of the street, while he once walked past looking proud and triumphant with a beautiful woman on his arm. But now she finds him alone, heartbroken: his love sailed away on a ship and left him behind.
Rather than pity him from a distance, she invites him in out of the cold, offers him a seat at her table, and gently coaxes him to laugh, sing, and dance again. It's a song about tenderness between strangers, and about choosing joy again after heartbreak.