My fiance is Swedish and is self conscious of how he speaks. Advice?

Okay, I’m 22, and I am a dance teacher. My fiance, Robert, is 25. He is from Sweden and he moved here with his parents when he was 18. We met in college and started dating. We moved in together two years ago and we got engaged 3 months ago, and I’m so excited to marry my best friend. He is sweet and kind and he makes me laugh, but he has some problems with anxiety and depression. He’s a graphic designer, so he works from home. Usually he likes to go out and be social, but he’ll have these days where he doesn’t want to go out because he is so depressed and anxious. It usually lasts 4 or 5 where he’ll sort of hibernate and won’t go anywhere. I know that a lot of his anxiety stems from how he talks and I sort of want to pinpoint that to start with. He has a thick Swedish accent and is very self conscious about it. He’s easy to understand; he just says a few words wrong or forgets a word sometimes. In private or with friends, he isn’t afraid to mess up the pronunciation of a word or say “what’s that word again?” but in public, he gets nervous. I can see the gears turning in his head every time he has to talk to a stranger, trying to think out the words and how to say them, and I can tell he’s nervous. He says that he’s afraid that people will think that he’s stupid. It’s sad to me, because I love how he talks; I love that about him. It doesn’t make him sound stupid at all, but he’s so worried all the time. He speaks very quietly in public and won’t mutter a word in Swedish, whereas when we’re at home, all I hear is him rambling on in Swedish in front of his computer or when he’s cooking. I don’t know how to help him get over this. What can I do? Or how can he help himself?