EU law requires all member states to recognise all EU passports and national identity cards throughout the FULL period of validity stated on them.
Some countries OUTSIDE of the EU have restrictions upon the validity of passports because they recognise that you could stay longer than planned in their country (e.g. because you're taken into hospital) and they require you to have a valid passport throughout all of your extended stay. However EU citizens have the right to travel to AND REMAIN IN any EU country, so having a minimum passport validity would make no sense. (i.e.you could arrive in Spain, to live there permanently, with just a few hours left on your passport. If you never intended to leave Spain it wouldn't matter at all).
It needs to be remembered that (with the exception of Ireland, which is legally 'trapped' by its open-border agreement with the UK) ALL other EU countries are full signatories to the Schengen agreement, which means that you don't need ANY form of documentation to travel between them at all. (It's only our stupid government which refuses to sign up).