It seems like the Captcha was the issue, but I couldn't determine what was causing the Captcha to fail. As a solution I got a physical card from the desk and loaded the weekly subscription onto it. This cannot be purchased from the machine, as you need a personalized card.
I think it's due to the VPN service I was using (WindScribe) When I got to France, I tried to open the account registration page, but it still threw the Error 15 page. The same error was thrown when I was connected to the EuroStar wifi. Only when I was connected to the wifi of my Airbnb was I able to get to the registration page again and the Captcha loaded.
For future reference of others, this is how it's supposed to look like:
