A very "general" link on the EU constitution :
http://news.bbc.co.uk/1/hi/world/europe/2950276.stm
Excerpt (I don't know how to use the quote feature):
"LEGAL SUPREMACY
What the constitution says:
The EU will for the first time have a "legal personality" and its laws will trump those of national parliaments: "The Constitution and law adopted by the Union institutions in exercising competence conferred upon it by the Constitution shall have primacy over the law of the member states."
What it means:
This really just confirms the status quo, which is that if the EU is allowed to legislate in an area of policy, its law will overtake any national laws. Equally in areas where it does not legislate, national law prevails. "
My question is what is left for domestic laws? It seems to me that the EU is legislating or controlling quite a few areas already.