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.