"Press freedom" historically means that the press can publish anything factual, artistic, or opinion based without fear of government censorship or retribution.
We are seeing the EU and various EU countries redefine fundamental terms for entirely different things, to the point where the original rights are completely eroded, and instead we have a system that effectively serves special interest groups in Europe.
An infamous example of this is the "right to be forgotten". In Europe there is now a process where individuals can effectively censor the internet/press from publishing factual information about their past transgressions. Ostensibly this is to allow the individual to move on with their life. For example, someone convicted of murder has successfully removed articles related to his murder from the internet (in Europe). This is incredibly dangerous. Why should the government get to decide what fact based censorship is irrelevant or not? I certainly think it is pertinent for society to know about past murders.
The EU is slowly eroding all individual liberties, while its markets are becoming less competitive and its welfare state expands to unprecedented levels. Free speech and freedom or religion are much worse in Europe. Germany is run by a Christian political party. In addition to no longer being able to advocate for Nazi politics in Germany, now you cannot speak about certain facts that have occurred in the past. Now France is attempting this novel "shake down of tech giants we cannot compete with" strategy, which is frankly a strategy that was until recently more likely to be seen in an Authoritarian country like China than the country that was the inspiration for the US independence.