I had the same problem. Upon looking in Console.app, it turned out the process responsible for verifying the app had actually crashed. That obviously shouldn't happen, and it seems like an OS X bug.
To work around this, open up Terminal.app (in /Applications/Utilities) and type the following:
Code:
xattr -d -r com.apple.quarantine /Applications/FINAL\ FANTASY\ XIV.app
(this assumes that you've installed FINAL FANTASY XIV.app into your root /Applications directory)
After typing that, hit return. When it finishes running, you should now be able to launch FINAL FANTASY XIV.app. What this command is doing is removing the information that tells the system that it needs to verify the application before running.
Before launching, you may want to open up Activity Monitor.app (again in /Applications/Utilities), search for FINAL FANTASY XIV, and if you find it in the list, select it and hit the (X) toolbar button and select Quit. This is because the verification process that crashed will most likely have left behind the frozen process.