Hmmm. Well, I'm pretty sure most people would use wedding bands, but, just as in the muggle world, there's nothing to say that they
have to use them. Again, most people would probably tend to, but perhaps Fleur didn't want to wear a ring. Or it could be part of her tradition to not wear one.
However, since we've seen both sides represented in the Potter books, you have pretty much free regin with it in your story. You could have your character not wear one, but you could have them wear one as well.
As for Hermione's parents, I don't think we know anything about them except that they're muggles and dentists. But, during the seventh book, they think they are called Wendell and Monica Wilkins and they live in Australia.
I hope I helped you some!
~Morgan
