For a challenge under the European Convention on Human Rights (to which Czechia is a signatory) the relevant articles are 10 and 17. Article 10, on the right to free expression, has the caveat that it:
may be subject to such formalities, conditions, restrictions or penalties as are prescribed by law and are necessary in a democratic society, in the interests of national security, territorial integrity or public safety, for the prevention of disorder or crime, for the protection of health or morals, for the protection of the reputation or rights of others, for preventing the disclosure of information received in confidence, or for maintaining the authority and impartiality of the judiciary.
This is analogous to Article 17(4) of the Charter of Fundamental Rights and Freedoms of Czechia (which has constitutional force by virtue of Articles 3 and 4 of the Constitution):
The freedom of expression and the right to seek and disseminate information may be limited by law in the case of measures essential in a democratic society for protecting the rights and freedoms of others, the security of the State, public security, public health, and morality.
The Strasbourg court has often had to consider this exception in the case of hate speech, promotion of terrorism, and display of prohibited symbols. In extreme cases, ECHR Article 17 kicks in:
Nothing in this Convention may be interpreted as implying for
any State, group or person any right to engage in any activity or
perform any act aimed at the destruction of any of the rights and
freedoms set forth herein or at their limitation to a greater extent
than is provided for in the Convention.
This has been held to limit the possibility of an Article 10 claim when the speech related to incitement to terrorism, Holocaust denial, political ideas incompatible with democracy, and other examples. For example, in Roj TV A/S v Denmark [2018], no. 24683/14, urging viewers to join the PKK and take part in guerrilla action was held to be over the line of Article 17. On the other hand, in Orban v France [2009] no. 20985/05, the banning of a book describing the author's participation in war crimes and lack of regret did not meet the standard, because the objective of the book was held to be contributing to a historical debate.
Paragraph 35 of the Orban judgement does admit that if there were an unequivocal goal of justifying war crimes such as torture or summary execution, then the result could have been different:
Il n'est pas douteux que des propos ayant sans équivoque pour but de justifier des crimes de guerre tels que la torture ou des exécutions sommaires sont pareillement caractéristiques d'un détournement de l'article 10 de sa vocation.
In a specific example of a prosecution and human rights claim based on the question, this is the kind of distinction which might be drawn, looking at the context of the prohibited speech. Results would depend on the speaker (journalist? politician? random person yelling in the street?), mode of speech, what they actually said, and so on.
If Article 10 were reached, then the court would examine whether the Czech law and its application were compatible with the caveat in all respects. A custodial sentence of three years might well be found to be excessive, as that is a significant interference with someone's freedom compared to (say) a fine. For example, in Cumpănă and Mazăre v Romania [2004], no. 33348/96, the Grand Chamber held (para 115):
Although sentencing is in principle a matter for the national courts, the Court considers that the imposition of a prison sentence for a press offence will be compatible with journalists' freedom of expression as guaranteed by Article 10 of the Convention only in exceptional circumstances, notably where other fundamental rights have been seriously impaired, as, for example, in the case of hate speech or incitement to violence.
Another important safeguard in Article 10 is the requirement that restriction must be "prescribed by law", which entails that a law must be "formulated with sufficient precision to enable citizens to regulate their conduct; they must be able – if need be with appropriate advice – to foresee, to a degree that is reasonable in the circumstances, the consequences which a given action may entail" (Centro Europa 7 S.R.L. and Di Stefano v Italy [2012], no. 38433/09). It might be argued that the law prohibiting approval of a "committed criminal offence" is not clearly applicable to actions in the international sphere where there has not been a criminal conviction.
In the same way, restrictions might be justified on the grounds of preventing disorder, or not: it would depend on whether there really is a public order danger. In Vajnai v Hungary [2008], no. 33629/06, wearing a prohibited Communist symbol (a red star) was held not to trigger "actual or even remote danger of disorder". Restrictions have been upheld for actions during protests where there was such a danger. Similar observations apply to the other potential grounds, such as national security or protecting the rights of others.
In summary, application of the Czech law could be found incompatible with the Convention rights, depending on the circumstances. The law is not incompatible on its face but it's the situation in a specific case which matters.
