Thank you, that's awesome!
I am a summer soup , oh ..

Oh, there's another song playing when he's smoking a cigarette near the end of that scene.
The Skyliners - Since I Don't Have You (1958)
Lyrics:
I don't have plans and schemes,
And I don't have hopes and dreams,
I don't have anything
Since I don't have you.
I don't have fond desires,
And I don't have happy hours,
I don't have anything
Since I don't have you.
I don't have happiness, and I guess
I never will again.
When you walked out on me,
In walked old misery,
And he's been here since then.
I don't have love to share,
And I don't have one who cares.
I don't have anything
Since I don't have
You, you, you, you
You, you, you, you
You, you, you, you
(Yo-o-o-o-o-o-o-ou)

Sorry you didn't get an answer for so long. Here's the song you're looking for:
A Thousand Stars in the Sky by Kathy Young & The Innocents (1960)
Lyrics:
A thousand stars in the sky like the stars in your eyes
They say to me that they'll never be
No other love like you for me
A thousand stars in the sky make me realize
You are the one love that I'll adore
Tell me you love me
Tell me youre mine once more (once more, once more)
Each night I count the stars in the sky
Hoping that you arent telling me lies
You're with me tonight, I'm captured by your charms
Oh, pretty baby, wont you hold me in your arms?
A thousand stars in the sky make me realize
You are the one love that I'll adore
Tell me you love me
Tell me youre mine once more (once more, once more)
Each night I count the stars in the sky
Hoping that you arent telling me lies
Youre with me tonight, Im captured by your charms
Oh, pretty baby, wont you hold me in your arms?
A thousand stars in the sky make me realize
You are the one love that I'll adore
Tell me you love me
Tell me youre mine once more (I'm yours)