Whoever transcribed this song has serious problems with French conjugation!

"tu m'appelles ton copain" sounds wrong to me. If it's a girl singing, she says "you call me your (male) buddy", as if he addressed her like a man! I would expect "tu m'appelles ta copine". I can't hear "copain", it's completely swamped by the music, but I can't think of any other word. The only explanation would be a song meant to be sung by a man later covered by a woman.
However, though "copain/copine" can mean "boy/girlfriend", here it means "(just) friend". It's a way of saying their relationship is over. So I would rather translate it as "ты зовёшь меня своим другом (а не любовницей)".
Funny thing is, the masculine "друг" is fine in Russian, while the feminine "copine" is expected in French.

Actually there is a problem with the title and first line.
"У тебя красивая улыбка" would be "tu as un beau sourire"
"avoir beau + verb" is a fixed expression meaning "no matter how hard you try (to do something)" or "regardless of (what you do)".
tu as beau sourire, tu es quand même triste -> как бы ни улыбался, тебе все равно грустно
j'ai beau essayer, je n'arrive à rien -> не важно насколько сильно я стараюсь, ничего не получается