You can ask them for a refund but there pretty high chance they can tell you no. Below is why.

All FFXIV Subscription Fees are non-refundable, with the limited exception in Section 4.7 below.
4.7 Refunds in Exceptional Circumstances Only. The entirety of your FFXIV Subscription Fee is applied by Square Enix to the FFXIV Service Account on the day that it is charged. All charges related to the Game are non-refundable unless third-party criminal activity is involved, as determined by Square Enix. Therefore, if you deactivate your FFXIV Service Account in the middle of a 90-day Billing Cycle, you will not receive a refund for the remainder of the Billing Cycle, but may continue to play the Game until the Billing Cycle ends.