So does the EU constitute a government? Well in some regards the EU has aspects of government.
In institutional terms the EU has an executive body, a legislative body and a judiciary – all features normally associated with government.
However, these bodies operate very differently from those within a national context and the Council, for its part, is composed of national governments. The EU certainly does not govern directly like the member state governments do. The EU cannot raise taxes and while it can pass legislation, it is dependent on state and sub-national governmental actors within them to implement it.
So, it perhaps makes sense to best think of the EU in terms of European governance. Please read this extract on governance and the European Union.
As you will see from this extract, the European space paints a complex picture from a governance perspective. While Europe does not have a European government, it is certainly governed by a multitude of different actors operating at different levels.