S'achève comes from the verb s'achever, meaning 'to end' or 'to finish'. While 'finir' is a common verb for 'to finish', s'achever often carries a slightly more poetic or definitive nuance, suggesting a natural conclusion or completion.
In the context of "Bleu De La Nuit," ZAZ sings, "Qui s'achève dans le bleu de la nuit" (Which ends in the blue of the night). It beautifully describes the day drawing to a close, dissolving into the tranquil blue of the night, making it a more evocative choice than a simpler verb.
Zaz builds the song out of the small things still intact. The wind in the trees — « Quand le vent caresse les arbres » ("When the wind caresses the trees") — a walk along the shore, and the fact that no one has yet turned this world into a country at war. The refrain draws the conclusion: « Que demander de plus » ("What more could you ask for") than one more day that ends in the blue of the night.
The second verse names the comparison the first one was making quietly. Elsewhere there are stained-glass windows set ablaze and cities broken open; here the ground is still free. The blue of the title is what that difference looks like from inside a safe country at the end of an ordinary day. Zaz sets a limit on it in the closing line — « Mais les nuits bleues ne peuvent durer toujours » ("But the blue nights can’t last forever").