Rengaine literally refers to an old, repetitive tune or song. However, it's often used metaphorically to mean 'the same old story' or 'the same old routine'.
In the context of the song, the artist sings, "Mamie est toujours sur le lit / À chaque fois c'est la même rengaine." This implies that his grandmother's condition is a recurring, sad situation, a 'same old story' that he hopes will change. It's a poignant word that captures a sense of repetitive sorrow and longing for something new.
This song is about noticing how fast the years go by, and making sure the people you love actually hear it from you.
The verses move between the rapper's own path (early years on the street, then seeing his own name on a poster) and quieter family moments: a grandmother who barely reacts anymore, a grandfather who says thank you with a hug on the shoulder instead of words.
The chorus is the whole point: don't forget to say 'I love you'. Life gets busy and people get older, so say it while you still can.