Congratulations!

Hello Daria!

My experience with Renfe is that if you call your credit card
in advance the transaction will go thru. Glad it happened for you! Its the best rate available

Renfe does accept PayPal, and they show they accept Amex cards, there are the Renfe issued cards only. (Asistente Virtual de Renfe)

Las formas de pago aceptadas por Renfe son: Tarjeta de Crédito o Débito, puntos de la Tarjeta +Renfe y Metálico (en Agencias de Viaje y Taquillas), a través de PayPal y a través de móvil con la aplicación Renfe Ticket. Las Tarjetas admitidas son:
VISA
VISA Electrón
MasterCard
6000-Maestro
6000-MasterCard
Diners Club
JCB Cards
American Express
Renfe-Visa
Tarjeta +Renfe
Si realizas tu compra por Internet y tu tarjeta es VISA o MASTERCARD, será validada mediante los sistemas de compra segura por Internet Verified by Visa o MasterCard

I couldn't get my CC to work on Renfe and I DID call my CC in advance. I don't think that's the issue, there is/was something about the way their software works that just does that, same as SNCF used to. Last year I could use SNCF fine, but for a couple previous years I couldn't. I haven't tried RENFE in a couple years for purchase, though.

But I never had a problem using RENFE when I selected the Paypal option, as that isn't processing your CC directly. I didn't want to use it, I preferred my own card, but I don't think that should ever cause a problem.