What it could offer was: you sit here and sell us cheap oil and gas, while we court all your neighbours to stop associating with you and associate with us instead. But it did not have any meaningful participation format for Russia, only that it should be increasingly lonely. Not to mention stuff like visa waiver or student exchange programmes. In the end even at the best of relations the integration was actually tiny.
When confronted with this, the West will usually deflect and blame it all on Putin, which is also not constructive: This does not offer any plan to a regular Russian, especially seeing how close EU politicians were to Putin at that time and how they did not care if he stays for as many terms as he wanted to.