Is it okay to re-friend the person I fell in love but didn't feel the same? Or should I leave it be?

I would say you should avoid her because it would hurt you very much and maybe even tear you apart. A friend of mine went through the same situation and decided to be friends with her, only to get a chance at her again after some time. The result was that it didn't work out as he planned and she came together with someone else. She didn't even tell him because she didn't want to hurt him.

To sum up I can only say that if she didn't love you before that she won't love you now or in the near future.

I hope I could help you and wish you good luck. It's a decision that you have to make and therefore it's really risky.

Ask yourself whether whatever benefits you had from the quondam friendship (which is not guaranteed the second time around, mind) would suffice to overcome the awkwardness / pain of rejection, knowing nothing would come of it romantically, possibility of staving off other prospects of relationship by clinging on.
You may not have a clear insight. It's a matter of intuition. Know thyself.
And then, you should ask them whether they are comfortable with the notion.