I never would've approached you...

I'm pretty sure he means he never would have tried to initiate a relationship with her, or "hit on her" as the current slang expression has it.

So he means his love for her is pure?

No, no. He means he thought she was out of his league. But I'm guessing here, without more context - does that interpretation make sense?

Willia: I think I have a crush on you.
Boris: Yeah, I thought you might.
Willia: Is it okay if I kiss you?
Boris: Yeah.
And after they kiss:
Boris: Willia... I never would have approached you.
Willia: Are you a shy guy?
Boris: Yeah.

In this case, I think Boris might perhaps mean that he was simply too shy to approach Willa. Or, perhaps, any girl.

Approach simply means 'move near', or 'go up to'.

In many cultures, people like having their private space. If I see someone sitting alone and feel the need to go up to them ( approach them ) I may feel the need to make an apology or excuse.

"I never would have approached you, but I saw that you were reading my favourite book."
It's often used as a way to go up to someone an

Thank you!