What about my right to search?
There is no such right, except in your imagination. There is a right (at least in my country, probably similar ones in the EU as a whole) to get information from publicly available sources. So the government cannot stop you from searching at all. But it can intervene in the information available if that information breaks laws. For example, copyrighted content, state secrets, but also information a court has found to be libel or slander.
And quite frankly speaking, for the cases this law is intended for (let's not focus only on the abuses, as most idiot journalists do because it makes for better headlines), the right of an individual to not have their life ruined by, say, completely made-up allegations of child abuse and rape quite clearly trumps your right of finding false and misleading information.