The EU far outdoes Russia in population, military spending, wealth, and technology. They don't need the United States to win a conventional war against Russia. The Russian advantage lies in unity and a European aversion to force. It may be advantageous for Putin to assert dominance over some of the former Soviet states. But an outright invasion of the EU? If anything would create a united front against Russia, that would be it. I don't know if Putin as after territory so much as maintaining a buffer zone against Western influence (and scoring the occasional political victory over the US).