I am French and I have a national ID card that expired recently. France extended the validity of this card and it is now valid for 15 years (instead of 10).
Why don't you redo it? It takes a week tops and it is free. Just go to your city hall and explain your situation; it will be free and quick.
Many European countries (the EU I think) accept national IDs of European citizens as a valid ID.
All of them, except outside Schengen they might be reluctant.
I would like to know which countries accept expired national French ID cards (expired less than 5 years ago) and in particular if Germany, Switzerland and Italy do accept these cards.
Once again, the better way to know is to contact the embassy of the countries you wish to enter. We don't need visas in Europe but maybe a valid ID is required (even though honestly unless you are traveling by plane they are not going to check).
Check online on the Embassy's website of Italy, Germany and Switzerland for similar problems or just call them.
Also here it says that he should rather get an "attestation de renouvellement sur papier à en tête (RF) avec votre photo d'identité agrafée dessus avec le Sceau officiel avec Marianne ".
Franchement ne t'embête pas si tu voyages pas en avion...