Most fan fiction are not freely licensed, but can a fan fiction/story be licensed under a free license, e.g. a CC BY license (or other Creative Commons license that allows commercial use)?
Does this also require the universe which this fiction is written to be freely licensed as well?
If you do not have a license from the copyright owners of the original work, then you're not allowed to make derivative work (like fan fiction - even though it may be tolerated). So in that case it doesn't really matter how you license your fan fiction.
If you do have a license to create derivative works, then you can slap any license on the new content that is allowed within the restrictions of the original's license. (For example, there might be a condition that any downstream derivative works should be non-commercial, which would mean you need to incorporate that clause in your own license.)
So, in general, I think you're correct that to put a free license on your fan fiction, there has to be a free license on the use of the universe it's based on.