EU law obliges all member countries to admit anyone who can prove that they're a citizen of an EU country (either by producing a passport or a valid ID card). The French officials would be obliged to let you in even if you only had 1 minute left on your passport.
The UK and Ireland are the only EU countries which aren't already full signatories to the Schengen Agreement (or about to become so), which means that passport controls have been effectively abolished throughout Europe. Ireland would like to sign the agreement but can't because the UK won't. (That's because of the existing 'open border' agreement in Ireland). If our government ever get their act together and sign up to what all other EU countries (and some non-EU countries as well) deem to be a sensible arrangement, you won't need a passport to travel anywhere in Europe.
Chris