This was an announced intention in April this year. The implementation of this decision probably needs further approvals and ratifications, and even after that, it takes time. The source material does not even exist, and I expect that in some EU countries collecting this data of all citizens will not be possible due to country legislation. Thus this is certainly far from complete, if even started at all.
It's safe to say that there is no database of 350 million EU citizens' fingerprints that anyone could copy.