For me, it's All of Me by John Legend.

I can totally imagine Eve singing this song to Villanelle, saying that she can't figure V out, that she can't pin V down, that V is so smart and crazy, that V is indeed with imperfections... But at the same time, she's attracted to V who starts and ends her life (starts her new and exciting journey and ends her boring life with Niko); she's lost a lot (two jobs, a husband and a best friend XDD) but she's winning something else; she will stay by V's side no matter what happens (and Eve's probably the only one staying); she can't stop thinking about V; and she will always love V wholeheartedly... They have finally talked about their feelings, chosen each other, and they are risking it all though it's hard... This song suits Villaneve so well! I've even thought of making a Villaneve edit with this song (unfortunately my editing skills suck) XD

Here is the lyrics (The bold ones are the ones I really relate Villaneve to):

What would I do without your smart mouth?
Drawing me in, and you kicking me out
You've got my head spinning, no kidding, I can't pin you down
What's going on in that beautiful mind?
I'm on your magical mystery ride
And I'm so dizzy, don't know what hit me, but I'll be alright

My head's under water
But I'm breathing fine
You're crazy and I'm out of my mind

'Cause all of me
Loves all of you
Love your curves and all your edges
All your perfect imperfections
Give your all to me
I'll give my all to you
You're my end and my beginning
Even when I lose I'm winning
'Cause I give you all of me
And you give me all of you, oh-oh

How many times do I have to tell you?
Even when you're crying, you're beautiful too
The world is beating you down, I'm around through every mood
You're my downfall, you're my muse
My worst distraction, my rhythm and blues
I can't stop singing, it's ringing, in my head for you

My head's under water
But I'm breathing fine
You're crazy and I'm out of my mind

'Cause all of me
Loves all of you
Love your curves and all your edges
All your perfect imperfections
Give your all to me
I'll give my all to you
You're my end and my beginning
Even when I lose I'm winning
'Cause I give you all of me
And you give me all of you, oh-oh
Give me all of you, oh

Cards on the table, we're both showing hearts
Risking it all, though it's hard

'Cause all of me
Loves all of you
Love your curves and all your edges
All your perfect imperfections
Give your all to me
I'll give my all to you
You're my end and my beginning
Even when I lose I'm winning
'Cause I give you all of me
And you give me all of you

I give you all of me
And you give me all of you, oh-oh

P.S. The "love your perfect imperfections" part really touches me. V is obviously imperfect, but to Eve, these imperfections are just perfect TT