A 'European army' would be under the control of... the EU? Some new organisation to be specifically created for this purpose? Some committee-designed scheme of rotating leadership between the main powers in Europe?
These are not spurious questions. Europe is a large and diverse place, far more diverse than e.g. the USA. Would such an army serve to protect Hungary as well as Spain, Sweden as well as the Czech republic, Poland as well as Germany? Even if some of those countries do not care to fall in line with the agenda set by the Eurocrats in Brussels?