Ordinarily, EU nationals do not need to show a national ID card or passport when travelling from one border-free Schengen EU country to another.
Even if you don't need a passport for border checks within the Schengen area , it is still always highly recommended to take a passport or ID card with you, so you can prove your identity if needed (if stopped by police, boarding a plane, etc.). Schengen EU countries have the possibility of adopting national rules obliging you to hold or carry papers and documents when you are present on their territory.
Under Schengen rules, in extenuating circumstances, where a threat to public policy or national security has been identified Member States are permitted to reintroduce temporary border controls.
Temporarily reintroduced border controls currently exist in Germany, France, Austria, Denmark, Sweden and (non-EU) Norway.
https://ec.europa.eu/home-affairs/what-we-do/policies/borders-and-visas/schengen/reintroduction-border-control_en