Good afternoon and thank you for posting on the Final Fantasy XIV Technical Support Forums.

I apologize for the delay in our response.

Has the error changed since you posted this? Does a wired connection resolve the issue?

There isn't much you can adjust on a PS4 to troubleshoot the problem, but you can double-check that your router has been reset by turning it off then back on after a few minutes. Also check that the following Port Ranges on your router/modem to ensure that they have been opened:
▼TCP
54992 through 54994,
55006 through 55007,
55021 through 55040
Your ISP can open these ports for you.

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