Both sides have a lot to gain from this. Russia doesn't want to be isolated again as it was during the Cold War, and Western Europe needs Russia Oil and gas. A mutual determination not to be divided and conquered would suit both parties.
We can't let the neo-cons (or the Russian hardliners?) win this one. "It's a mystery to me - the game commences, For the usual fee - plus expenses, Confidential information - it's in my diary..."
Your suggestion of a friendship and cooperation treaty between the EU and Russia is probably the best option
That's what I proposed in my half-drunk speech in Nizhny-Novgorod... "Dieu se rit des hommes qui se plaignent des conséquences alors qu'ils en chérissent les causes" Jacques-Bénigne Bossuet
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.
