More players (including me) are reporting the same issue through the Technical Support section of the Forum: "Technical Support > Launcher Connection Error".

By the looks of it, the traffic that goes through Amsterdam (NL) to "*.square-enix.com" are experiencing the issue. Mostly because the problem isn't isolated to just the game, but the website, Mogstation, Customer support site and the official forums.

Players are circumventing the issue by using a (free) VPN application and making a connection through a different country. At least, up till the point you've gone through the Authentication process and are ready to start the game.

But, what ever you do, don't reinstall the game! The Client will need to be downloaded from the same location where the issue is related to.