In the end, I found the song!!!!

In fact, I've listened to a tune for a classical American film series on TVE1 channel several times and since then, I can't stop humming it! It's used as the soundtrack for a tv teaser and it's so catchy that I couldn't help surfing the net to find out about its author. Indeed, John Mayer is supposed to be its composer and Lana del Rey seems to have sung it inspired by an older version. I'm not very sure about that, but anyway, I'm still looking into it. Any information about this issue will be welcome. Meanwhile, let's enjoy!