From http://en.wikipedia.org/wiki/Europeana#Financing

Which seems to be direct from the Europeana web site itself (something that seems to breach Wiki's own rules of sourcing, but never mind!)...

Europeana and the projects contributing content to Europeana.eu have been funded by the European Commission under eContentplus, the Information and Communications Technologies Policy Support Programme (ICT PSP) and similar programmes. In order to participate in a wide range of projects, which are only funded by the Commission for 50-100% of the costs and do not include overheads, Europeana is also reliant for an element of its funding on Member States' ministries of culture and education.

Which is of no help in telling us if you as an end user have to PAY for anything....