"The European Court said the conviction was correct"
First of all, I think the argument that can be drawn from one Court decision is not very strong.
Second and possibly more important: this was a decision by the European Court of Human Rights (which is completely unrelated to the European Court of Justice and the EU) and the decision was not an appeal but the question was whether Austria had violated the European Convention on Human Rights which is a specific international treaty with specific Rights, mainly crafted in the late 1940s. It doesn't aim to be an all around Constitution for Europe but protects certain things for example in this case possibly free speech under Art. 10.
The fact the the HR Court interpreted the Convention in a way that allowed Austrian Authorities to fine a certain statement does in no way imply that freedom of speech is not protected in the European Union or in the Council of Europe Member States. Instead it is a fundamental idea of the European Convention on HR that states get a certain margin of appreciation to make decisions such as these. In other cases (for example concerning whistleblowing or Lingens v Austria) the Court has upheld free speech.
The EHCR, not the ECJ (the latter of which is related to trade agreements). The EHCR did the opposite of invalidate her conviction -- they upheld the decision of the Austrian court[1]. In other words, they rejected the claim that Austria's anti-blasphemy laws are a violation of human rights (which I disagree with -- though I'm definitely not anti-EU like others in this chain).
You should understand the framework around this whole thing, since it involves religion (ancient, fictitious or otherwise very hard to prove, very little actionable evidence, mostly based on belief), but also current laws and crimes (well documented, easy to provide evidence).
First of all when you make an accusation you have to prove it, bring actual evidence, otherwise it's slander (or blasphemy, in a religious case). Second, we're talking about religion, so take every detail (the "evidence") with a grain of salt. Third, even assuming you can use a holy book to prove your case, the accusation is not valid because the law you're using wasn't in place back then when the "crime" was committed. On the other hand a blasphemy law is in place when your crime was committed.
So although I'm as far from a religious person as it gets, I still believe people are entitled to their own religious beliefs without someone uselessly dragging them through the mud. Every religion mentions some details that could prove insulting for many people, why bring one up in particular? And if a law is in place don't break it arguing that it's unfair. Maybe fight for changing it before you break it.
