There’s a significant detail which is missing from this analysis. The law which puts copyright over privacy is a French law, not an EU law. The EU court found that the French law doesn’t contradict any EU law.
So the EU court did not determine that copyright is more important than privacy. It determined only that the French parliament is allowed to decide that question for France.
So while this does set a bad precedence, it is not as bad as the title would like you to believe.