More formal trade links and - perhaps more usefully - sharing of technology and innovation could have more of an influence.
What makes Russia strong at the moment is that it has already fallen apart - and it didn't. The vassal states split off, but there was no internal East/West split. So today's Russia has a strong and coherent political identity which would swamp that of the EU.
Russia will calm down, at least for a generation or so, if the US stops being aggressive and confrontational. The problem isn't on this side of the Atlantic and can't be solved here.
