Vincent Reynouard will be extradited from Scotland to France for what is described as 'holocaust denial' see - https://news.sky.com/story/french-holocaust-denier-vincent-reynouard-faces-extradition-from-scotland-12983203.
Mr Reynouard's barrister opposed the extradition application, arguing that 'holocaust denial' is not an offence in Scotland or anywhere else in the UK.
However, in granting the Application the judge held that the acts Reynouard is accused of, would be a criminal offence in Scotland under section 127 of the Communications Act 2003, even though holocaust denial is not an offence per se.
This may be a significant development, as it means that a person can be extradited for something that is not an offence in the UK, but where the acts they are accused of would amount to a wholly different offence in the UK. Section 127 above is concerned with communications that are menacing or grossly offensive.
I do not know how the French law is drafted (hence why I put 'holocaust denial' in inverted comas, as I do not know precisely what one has to deny to commit the offence), but understand that it is concerned with denying crimes against humanity and thus appears to have an explicit political aim, unlike section 127 which on the face of it, would appear to be aimed to prevent distress to particular individuals.
In the early 2000s, I recall the Bruges group expressing concern about this exact scenario in relation to the European Arrest Warrant and such concerns being dismissed.
It is noteworthy that the Second World War ended 78 years ago and that it is not a crime to deny any other genocide.
Those who support laws against 'hate speech' will often argue that the issue of free speech is philosophically complicated and that there has never been absolute free speech.
However, offences against inciting violence are easy to justify and to distinguish from 'hate speech laws'. Further, the other established exceptions to free speech, such as offences for Contempt of Court, are designed to prevent specific and direct harm; they cannot be said to have a political or ideological aim
In contrast 'hate speech laws', or laws such as the French law, have political and ideological objectives in mind and they are not designed to prevent specific and direct harm.