As a national of a European Union member country, you can work or seek work in another EU country.
From the 1st of January 1992 citizens of every country in the European Union and the European Economic Space were able to seek work in any member state.
Provided they are not self-employed, they are subject to the same legislation as similar workers in another state.
Every citizen of the European Union can access public employment services.
More information:
http://ec.europa.eu/youreurope/nav/es/citizens/working/finding-job/index.html
Working at European institutions:
http://europa.eu/epso