Chavire literally means 'capsizes' or 'overturns', often used for a boat. It's a vivid and somewhat dramatic verb not commonly found in everyday conversation or every song.
In this song, Aznavour uses it metaphorically in the line "J'ai le cœur qui chavire" (My heart capsizes). This powerfully conveys a feeling of being overwhelmed by emotion, as if his heart is being turned upside down by love, fear, and longing. It's a unique way to express intense emotional turmoil.
"Ă€ t'regarder" is a quiet, aching love song. The singer spends the day far from the person he loves, and it's only at night, when she comes to sleep beside him, that his whole world narrows down to one thing: watching her.
Just looking at her stirs up everything in him at once. His heart sighs, races, and aches. He wants to cry out, sob, or laugh, all at the same time. It's the kind of love that feels almost too big to hold quietly.
Near the end, the tone shifts from tenderness to real fear. He imagines her dreaming of someone else, and the thought is enough to make him want to shout it all out, to fall apart, to cry "I love you" into the night. It's devotion pushed right up against the edge of losing her.