I don't want to touch the consent/rape aspect of this. I will say (and this is not me blaming you here - this is just what I would consider if I were your SO) the texts between you and the friend and the fact that you saw his stolen glances would look very suspicious. People tend to see what they want to see, so I couldn't tell you if the "friend" is truly predatory, if he honestly felt like you were reciprocating before the incident, or if he is just scrambling to make you the scape goat. Since you can't remember what happened that night, your guess is as good as his or your boyfriend's as to whether or not you would have had sex with him. There's a first time for everything, and no one is a cheater until they cheat. In addition, good people can do bad things. No one is wholly innocent or evil. You may not have intended to hurt your boyfriend, and you probably would have outright declined any advances while sober, but you did hurt him. The point of all of that is there's no sense in picking apart what you could have done and why or why not. No one can confidently give an answer (maybe aside from the "friend," but that doesn't mean he's correct even so). Your relationship will depend on what you do from now on, not what you might have done then.

A good start to fixing things would be limiting or totally cutting out alcohol. No one deserves to be taken advantage of while inebriated, but why put yourself in that position to begin with? Getting wasted often leads to fights, mistakes, and hangovers. Imbibe as if you may have to deal with an emergency - because you never know. If you're in control of at least yourself (I recognize you can't always prevent something happening to you), then at least you'd be able to know what your intentions are/were.

Cutting out the "friend" is another excellent plan. In addition, should something like this ever happen again you should tell your boyfriend if you feel like someone is nursing a crush on you. That situation could have been shut down weeks ago. Again, you can't account for the friend deluding himself into believing you like him, but it'd be a hell of a lot easier to rebuild your relationship if your boyfriend knew the guy was instigating and you were able to show him a text that said something along the lines of "I want to be clear that boyfriend and I are in a monogamous relationship and I don't want to do anything to jeopardize it, so these are the boundaries I'm establishing (such as not getting wasted together)."

Rebuilding trust takes time, communication, and consistency. There's no magic phrase you can say that will flip a switch and make things go back to normal, so don't try. Understand you're looking at months of work here, not days. Talk to your boyfriend, build a plan together that prevents this from happening again, and let time do the rest. Don't agree to anything you won't be able to fulfill. Giving him bad news is far better than promising something you can't uphold. Honesty is more important than appeasement.

Beyond that, the choice is his. The best you can do is work on yourself, and then you'll be in a better place with or without him.

Best of luck.