Thank you for the reply Dr_Cheesesteak.

I believe Steam can natively use the PS4 controller, but it may have to be configured in Big Picture Mode first. If your Xbox 360 controller works without issue, you may have to configure it with Steam. Open Steam and select 'Steam' in the top left corner then go to 'Settings'. In the next window, select 'Controller' and then 'General Controller Settings'. Here, make sure 'Playstation Configuration Support' is checked (if it is already, try unchecking it and checking it again).

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