Unfortunately the person above is right and you cannot get a refund for subscription time.

When you cancel a subscription, you should get an email with the title "[Square Enix Account] FFXIV Notification: Subscription Canceled". If you do actually have that, then you might actually have a chance of getting a refund.

Although saying that, they also send out an email 5 days before "[Square Enix Account] FFXIV Notification: Upcoming Payment" to let you know that a payment is coming out...

Sorry I think you're out of luck