I ran into this useful article about how names and title cannot be copyrighted, only the complete work. So I'm not too worried about the title as my story is completely different from Alice of Wonderland in Paris.
http://www.plagiarismtoday.com/2010/01/08/5-things-that-cant-be-copyrighted/
Copyright doesn't apply to titles or names, but trademarks can. That will depend on how broad of a trademark Disney has applied for (eg movies, books, shirts), and if there can be any arguments depending on the medium, or how similar a name can be.
I think there have been a few trademark cases where names were too similar within the same product market.
Disney holds copyright over their versions of the "Alice" story, and trademark over the titles - but not the original. The owners of "Alice of Wonderland in Paris" could argue trademark infringement because of the similar titles leading to possible confusion by customers that the deck is in some way associated with the movie.
There are actually issues that affect Disney regarding copyrights. For example, the reason US law has extended copyright protections today to a length of time that was NEVER intended when copyright law was created is because of petitioning by the Disney Company and others - if it wasn't extended, "Steamboat Willie", featuring the first appearance of Mickey Mouse, would be a public domain work today. And I can bet that when 70 years after Walt Disney's death approaches, they'll be petitioning to push the expiration date of copyrights even further. It doesn't matter if Mickey himself is a Disney trademark - you could legitimately sell works that are copies of "Steamboat Willie" or directly derived from the cartoon short.
It's how the original "Little Shop of Horrors" movie, directed by Roger Corman, became a play, then a movie based on the play - at the time the original work was created, you had an automatic copyright for 28 years with an option to renew for 28 more. Corman failed to renew - in interviews, he sort of describes it as having slipped through the cracks - and it became part of the public domain, with Corman not being entitled to any profits from the derived works nor having any control over those works. The renewal has since been removed.
Current US law is that a work will be covered by copyright for the either a) 70 years after the death of the creator, in the case of individually-created works, or b) in the case of corporate authorship, the shorter of either 1) 95 years after publication or 2) 120 years after creation. This only covers works created in 1923 or later which were still covered under copyright law (not in the public domain) in 1998. Anything created prior to 1923 is already in the public domain. There's a special exception carved out for works created before 1 Jan 1978 but published in recent history at the time the current law was enacted (1998), so those works may be protected until as long as the end of 2047.
As I'm sitting here thinking about this, it's very possible that the movie in question is actually in the public domain by now - if the creators let the US copyright lapse before 1998.
