Yes it's OK - it just needs to be valid. Same as anywhere else in the EU.
Still a good idea to renew though - you won't lose anything as the unexpired validity will be tacked on to the new passport and if there are any fee increases in the pipeline you'll avoid them.
you should be fine,we went to france in 2005 with my wife knowing her passport was going to run out while we were there,we did try to get a new one but would never have managed it as my son also need his own passport(he was on hers) so we went anyway. comming home all we got was a wag of the finger and a tut tut from the french gendarme/customs person and then he waved us on.
on the english side we mentioned it and she/he said its ok dont worry.
Eu passports are valid in all EU countries up to the date of their expiry.
However, a tour operator, travel agent, or airline might require that a passport be valid for 3 or 6 months after the date of your return.
Check.