We do pluralize. Even euros. But the EC has tried to make “euro” an invariable name (wanting it to be the same in all countries for all languages) and so some are following that suggestion.

Note “80 dollars” or “50 euros” without a “de” (but “centimes d’euro”).

See also here on Wikipedia (in French).

In all EU legal texts, the nominative singular spelling must be ‘euro’ in all languages (‘ευρώ’ in Greek alphabet; ‘евро’ in Cyrillic alphabet). Plural forms and declensions are accepted as long as they do not change the ‘eur-‘ root.

So, saying 50 euros is correct as the root remains unchanged. Funnily enough, it’s not in the TLF but it looks like the Académie said it must be pluralized. (Note also that one shouldn’t pronounce cent the English way, but the same way as 100.)

Le Lexique des règles typographiques en usage à l’Imprimerie Nationale indique que les valeurs monétaires doivent s’accorder au pluriel, et que l’euro n’est pas plus une exception que le franc. On dit donc :

3 euros

A noter qu’il précise également que si la division officielle de l’euro est le cent, il est toléré, voire encouragé d’utiliser le mot “centime”, qui est lui aussi variable :

3 euros et 6 centimes