I'm going to assume you were using an older version of Windows (Windows 7 perhaps?), in which case, when you install a new version of Windows it basically requires all your programs to be reinstalled as well unfortunately, including FFXIV (this is why I loathe updating to new versions of Windows, but sometimes it's unavoidable).
Sadly you will have to reinstall the game again for Windows 10, there is no way around this I'm afraid.![]()