Rengaine translates to "refrain" or "old tune," but it often has a more specific meaning. It describes a phrase or melody that is repeated so often it becomes tiresome, like an old song you can't get out of your head.
In the song, Céline Dion sings about "sa rengaine insolente" (its insolent refrain). She uses this word to personify the stubborn, repeating voice of her inner child, which powerfully illustrates the song's theme: you can't escape who you truly are.
This is such a beautiful and honest song from Céline Dion. The whole idea is right there in the title: "On ne change pas" [We don't change]. She argues that no matter how old we get or what we do, our core self, the child we once were, is always there. We just learn to hide it better. She says we "met juste les costumes d'autres sur soi" [just put other people's costumes on], but these disguises are never perfect. A jacket or a tough attitude can't completely hide the real person underneath.
What I love is how personal she gets. She sings about a "petite fille maigre" [skinny little girl] from her hometown of Charlemagne who is still with her, watching her put on makeup and almost laughing at the attempt to hide her. It's this idea that no matter how famous she becomes, that worried little girl is still a part of her. The song suggests that deep down, we're all still that kid, and our true nature will always peek through in small gestures that "trahit qui l'on est" [betray who we are].