Thank you for the reply Spakkum,

The game will check for an update before starting the game. If you cannot connect to the server properly and complete the version check, you will get this error.

There are a couple things you can try. First, try resetting your router by turning it off and back on. Make sure that any anti-virus or firewall program you use has an exception for Final Fantasy XIV (if you have trouble with this, you can also temporarily disable them). Check the following Port Ranges on your router/modem to ensure that the following Port Ranges have been opened/forwarded/triggered:
▼TCP
54992 through 54994,
55006 through 55007,
55021 through 55040

*You may learn how to do this by visiting http://www.portforward.com/
Find your specific router's brand and model number from the 'List of Routers' and you will be provided a step-by-step guide on how to access these port settings.
Otherwise, your ISP may forward these ports for you.*

We hope we can be of assistance in helping you enjoy the exciting world of Final Fantasy XIV!