You're right, your relationship is going to change somewhat. It's inevitable when people couple up. But that doesn't mean you'll lose him, just that you'll have to work with him to hang out, that's all.
Remember that you're not alone: a lot of guys have wives and best friends who don't necessarily get along. But assuming she's not a utter troll or jealous control freak, she should be OK with him hanging out alone with his best friend. Just stay in touch on the phone and online, and work out times to hang: more of this will have to come from you, but he'll want to hang.
If she IS a jealous control freak, well, that's something he needs to handle.
Either way, good luck!
A great way to maintain your friendship with your friend would be to work on the relationship with his fiance and future wife. She is special to him, and at the end of the day, she must come first, even before you. By taking the high road you demonstrate you also place value on their relationship. Not knowing the underlying cause of you and her disagreement, I'm gonna assume it's not totally irreconcilable. Reach out to her, tell her you realize you both had your differences in the past, but you are willing and wanting to put that behind you. Heck, you could compliment her on her taste in men, since I'm assuming you think highly of your guy friend. He clearly sees good things in her, so try to yourself.
Even if she does end up rebuffing your attempts to reach out, at the very least, you can take comfort, at least you tried.
I would *not* be cool at ALL if my husband was hanging out alone with his best female friend who can't stand me. Similarly - I would respect my husband enough not to hang out alone with my best male friend if he hated my husband.
If someone I'm friends with harbours a hatred, shows a dislike towards or "cant stand" someone in my family or my relationship - I personally would not want to be around them or have them in my life. It is also not fair for you to put the guy in that position! Maybe I'm too loyal but thats how I would feel.
I also got the vibe that the questioner was a female, and having recently become engaged, I saw this question and thought it would help me see it from by fiance's best friend's side. Although the answer seems tailored for male best friends, I see where you are coming from.
A problem for me though is that my guy best friend is also my ex (but completely platonic now, it was years ago). So when a bunch of us hang out and my fiance and best friend talk, they inevitably begin to talk about me, and.... *compare* if you know what i mean. It bothers me but at least my FH is open to me still talking to him.