There is no European nationality or citizenship. You're a Belgian citizen and hence a Belgian national. IF your state (not government or country!) allows dual citizenship
, you can apply for it. Otherwise you and/or she has to revoke yours / hers. That has nothing to do with the Schengen agreement. These are things that you need to enquire from your authorities. None of the successor states of the USSR or the CIS allow dual citizenship.

The only exception - as yet - are children born to citizens of two states, and can have two passports.