How does Europe orchestrate the various national budgets?  

The crisis that started in 2008 had many causes but it didn't help that all the countries that have been doing their own bookkeeping and budgeting in isolation. So, in 2010, when the European Union defined its new strategy for growth, the objectives included better coordination of national policies in the area of: budget, growth and employment. The Member States and EU institutions now work closely together to a precise timetable during the preparation of the national budgets. This process, known as the European Semester, allows the EU to keep a close eyes on the countries. All these institutions have their say on the subject. 

First, the European Commission sets the priorities of the EU for the year ahead. The European Parliament and EU Council then discuss and approve them. At the beginning of every year, each Member State is scrutinised on their economic situation, their reform programmes and potential imbalances. The EP can invite the presidents of the other institutions to discuss issues related to the European Semester and call for dialogue with Member States. At the spring meeting of the EU Council, the heads of states and government set the economic and fiscal guidelines for the EU. It's the up to Member States to follow these in: their reform agenda and their plan to guarantee sound public finances. The EU institutions the review the economic situation and policies of each state and issue country specific recommendations. Then the States have to follow these recommendations when drawing up their national budgets. 

Credit to European Parliament