No, if you don’t change your passport you only have to scan your fingerprints once in the EU.
I have just returned from the EU last week and I have been fingerprinted twice — once on entry and once on exit.
The US passport holders get fingerprinted on entry only, as I’ve heard.
i just traveled to the EU last week and you're wrong, got fingerprinted on entrance and exit
If you have a recent EU passport (like 6-8 years), biometrics like fingerprints are already in the chip, and you won't need to be fingerprinted upon arrival or departure, at least in theory, I wouldn't be surprised if some bureaucrat decided that the passport data can't be trusted and we'll fingerprint everybody anyway.