There are a lot of lessons to be learned here, and I think the most important one is to be proactive in keeping your relationships healthy.

I've seen some other comments telling you that your friend was not a "real" friend. Imo, playing the blame game is the wrong perspective for your own growth as a person. For your own benefit, it's important to recognize that you could have taken action to prevent this situation from blowing up.

What you should have done before shit hit the fan:

1. Tell your friend to stop when you found out about the rumors, and make them know you're serious. Your friend was basically acting with your tacit permission when you simply let the rumors be.
2. Tell the girl about the rumors yourself. Just apologize for the trouble and say that you're actively trying to kill the rumor. Example:
   "Hey [name], this is Impossible_Tale_2173 from [uni course]. I want to apologize for any rumors you may have heard about you and I sleeping together; I didn't start them, and I'm actively trying to clear up the rumor. Let me know if there's anything you'd like me to do."

What you should have done once shit hit the fan:

1. Admit your fault to the girl, explain your inaction in terms of stupid but harmless wishful thinking, and let her know that you're willing to make it up to her. Example:
   "Hey [name], I'm sorry that you heard rumors about you and I sleeping together. I didn't start them, and honestly I was just hoping for them to blow over quietly. In hindsight, I should've told you earlier and done more to squash the rumors. Let me know if there's anything you'd like me to do, I'm clearing up the rumor whenever I hear it now."
2. Don't try to pass off the blame of the matter. Don't make it weird and give the girl reason to think that you started the rumor.

What you should do now that you've lost a friend and ruined things with the girl:

1. Do some forward thinking for christ's sake. What was the endgame of letting the rumors be? Did you think the girl would appreciate you more for the rumors? Did you think the rumor would make you look cooler to your peers?
2. Move on in life, don't be petty about it to the friend or the girl. This seems bad now, but it's not so bad in the grand scheme of life. You didn't ruin a committed relationship, you're still young, your friend may not have been the best company etc.
   Most important is to make sure this sort of thing doesn't happen again, take it as a painful life lesson. You're not a helpless victim at the whims of your peers, proactively do the best thing for you.