The situation is actually a mess. Here are only some of the relevant bits from Wikipedia:
Official practice for English-language EU legislation (not necessarily in national legislation) is to use the words euro and cent as both singular and plural. [...] Because the s-less plurals had become "enshrined" in EU legislation, the Commission decided to retain those plurals in English in legislation even while allowing regular plurals in other languages. The Directorate-General for Translation now recommends that the regular plurals, euros and cents, be used. The European Commission Directorate-General for Translation's English Style Guide (a handbook for authors and translators in the European Commission) previously recommended the use of regular plurals for documents intended for the general public but now has no restriction on usage[.]
Prior to 2006, the inter-institutional style guide recommended use of euro and cent without the plural s, and the translation style guide recommended use of invariant plurals (without s) when amending or referring to original legislation but use of regular plurals in documents intended for the general public.
As the euro was being adopted in Ireland the Department of Finance decided to use the word euro as both the singular and plural forms of the currency, and because Irish broadcasters took their cue from the Department, the "legislative plurals" tend to also be used on the news and in much Irish advertising. This has had the effect of reinforcing the s-less plurals, although advertisements made in the UK for broadcast in Ireland tend to use the plurals euros and cents.
Common usage in the rest of the English-speaking world, where the euro is not the local currency, is to use the -s plurals. The media in the UK prefer euros and cents as the plural forms. Broadcasts of currency exchange rates outside of the European Union tend to use the plural in -s, with NPR in the United States and CBC in Canada being two examples.
So, both plural forms are correct. Just go with whichever your audience is more accustomed to.