"You have no right to enter a country where you are not a citizen, regardless of what treaties and protocols your two nations have set up."

According to the EU:

"The first right of a European citizen is the right to travel, work and live anywhere in the Union."

http://europa.eu/abc/12lessons/lesson_9/index_en.htm

I guess that's because the member states of the EU have given up complete sovereignty through things like the Treaty of Maastricht.