Actually the situation is a bit different.
According to ATCEUC the organiser of the action ( the first co-ordinated Pan-European ATC action) the action will take various forms in various Countries / centres but all on the 19th of June..
For instance :
Italy and Greece will go for a 4 hours strike between 12 and 1600 local. Portugal will go on strike between 11 and 1500 local and France will go for a 12 hours strike. ( But the legal minimum service will apply )
Budapest airport will be closed 3 unspecified hours that day. etc...
Most ATC centres Unions will support the action ( with some notable exceptions of course..) , so chances of re-routings that day could prove very difficult.
The main reason for the action is to show the EU commission that European controllers a a whole are against the new PROPOSED RULES OF COMPETITION IN ATM as laid down in the revised draft for the Single sky initiative.
A nice day to plan for maintenance I guess....