I too feel your colleague was overreacting (i'm black myself) I to would feel bad for the man your talking about. People make mistakes and say nasty things in an argument that they would never say to some one in day to day life. I think he should have gotten some support.
Anyways about your colleague i'd just say pull him to the side and talk to him. Tell him how you feel and say that me feeling bad for someone who needs help is basically in my nature, (work in health) people make mistakes, yep even racist ones and still deserve a second chance. Let him know that him going to your manager, (without proof and before talking to you about it) and saying your racist is sooooooo rash and could of been detrimental for your career.
Don't let him go around and spread rumours about you being racist, shut it down in a civilised way.