Either disintegrate the currency union, possibly Schengen as well, and let each country govern itself as it sees fit (seemed to work quite well 20 or so years ago) - simply by the virtue of common European heritage and values (at least compared to the rest of the world - China, US, Muslim countries), we'll end up collaborating quite well.
Or establish a United States of Europe, where the federal government takes care of the budget (no more "Greece defaulting" and "Cypriot capital controlls"), military (no more "UK intervention in Syria") and probably a few other things. Of course, to implement this, we need to agree on a common set of values from the beginning, which IMO we should model on Germany/Switzerland/Denmark (i.e. direct democracy, strong military but non-interventionism abroad, publicly-funded schools and healthcare but allow private services as well, strong consumer and environmental protections, flexible employment but with a strong social net). Personally, I'd add freedom of speech and the right to self-determination (secession) as well, but most of Europe seems quite opposed to that...
Germany has the biggest population and the most wealth.
The smallest countries seem to do well, too.