EU Marriage certificate

Welcome to the expat.com forum and good luck with your move to Spain. Barcelona which is a lovely city, lucky you!

You might have already done this, but typically you need to do two steps:

First, you become a legal Spanish resident by doing your EU Citizen Registration (little blue/green card, or mine was), thanks to your Greek citizenship.

https://extranjeros.inclusion.gob.es/es/InformacionInteres/InformacionProcedimientos/CiudadanosComunitarios/hoja101/index.html

Second, you apply for "family reunification" for your non-EU spouse.

https://extranjeros.inclusion.gob.es/es/InformacionInteres/InformacionProcedimientos/Ciudadanosnocomunitarios/hoja012/index.html

As part of this second step, you would provide proof of the family relationship. If you're married this would be a marriage certificate.

I've personally not heard of a "EU Marriage certificate" or "multilingual marriage certificate". But I don't believe this is what you need.

Instead, I expect that what you do need is your original marriage certificate AND you need to get it legalized (or maybe apostilled, depending on where you got married) AND you need a translation into Spanish (probably a certified translation by state-registered Spanish translator). Here's the relevant snippet from the 2nd page above:

"Important note: when documents from other countries are provided, they must be translated into Spanish or the co-official language of the territory where the application is submitted. On the other hand, all foreign public documents must be previously legalized by the Consular Office of Spain with jurisdiction in the country in which said document was issued or, where appropriate, by the Ministry of Foreign Affairs, European Union and Cooperation, except in the event that said document has been apostilled by the competent Authority of the issuing country according to the Hague Convention of October 5, 1961 and unless said document is exempt from legalization by virtue of the International Convention."