Often times authentication errors are due to the company's inability to process your specific credit card. Be it that the card information was entered incorrectly, or the card number and billing information are incorrect or mistyped, or you are attempting to use a card that the company does not accept (certain cards arent as widely accepted as Visa or MC), and as Grimmel mentioned, if you try to use a NA credit card on the EU store it may not work either.

Square Enix's store however does offer paypal, which can be a good work around if your card is not accepted. Paypal acts like a middle man for you. I dont know if you have a paypal account or not, but it is worth a shot, and many companies accept Paypal online, so its worth it to have.
That being said, if you dont want to use Paypal and your card is accepted by Amazon.com you can buy the digital copy of Heavensward here if you have an NA account: HERE
Keep in mind however, that Amazon has not yet released their preorder bonus codes, whereas the Square Enix store codes are now available to enter on Mogstation.