Broyer du noir is an idiomatic expression that literally translates to "to grind black". It means to mope around, to be in a dark mood, or to dwell on negative thoughts.
In the song, Amel Bent sings, "Passer les hivers à broyer du noir" (Spending winters moping around). This vivid idiom paints a picture of someone consumed by sadness and melancholy, making it a memorable and evocative phrase to learn.
Amel Bent starts by admitting how bad things got: "Passer les hivers à broyer du noir" [spending winters brooding over dark thoughts] and years spent chasing numbness through "la tournée des Enfers" [the tour of hells]. Then the chorus turns that confession toward one person. "Il n'y a rien que je fasse mieux / Que t'aimer, que de t'aimer de trop" [there's nothing I do better than loving you, than loving you too much] is the whole song in two lines. She isn't proud of loving this hard, she just doesn't know how to do it any other way.
The second verse tries other people and comes up empty. Other mouths and "cœurs trop froids" [hearts too cold] leave her catching a cold instead of anything real, "J'ai chopé la crève, ô combien de fois" [I caught a cold, so many times]. Other loves just knock her off balance, "Comme un vertige, tomber en arrière" [like a dizzy spell, falling backward]. None of this gets resolved. The song keeps circling back to the same chorus, and by the last repeat the closing line has grown a third "que t'aimer" tacked on, as if saying it three times is the only way she can make herself believe it.