Then ACTA will be ratified by the EU Parliament (i.e. the legislative branch).
Then ACTA will be ratified by national Parliaments. (Where necessary - most likely in all EU countries. A little different story in U.S., where Obama can just put it into law by executive order, because treaties that don't change U.S. law don't need to be ratified by Congress.)
The ratification in EU Parliament is what really counts, because 80-90% of ACTA text applies to EU law, and only a fraction applies to national law. (The latter primarily with regards to criminal prosecutions, which obviously are strictly national jurisdiction.)