2 things
1) the euro zone is specifically talking about a monetary union (I.e. use the same currency). So if it breaks up, technically the European union would still exist. Denmark and Britain not in the euro but still part of the European union. So the breakup of the eurozone will have no effect on licences.
2) the JAA (as a quasi regulatory authority) ceased to exist in 2008. Replaced by EASA
Facetious I know.
In reality if Europe were to cease to exist as a political union either there would be grandfather rights or many airlines would be grounded due lack of flight crew.