They can say whatever they want, but the UK can't conduct an extra-territorial police action in france. They can bar subject from traveling to france instead. The onus is on the UK.
[1] https://www.courtlistener.com/docket/71209929/1/4chan-commun...
4chan does not reach out to UK users in any way, only responds to their incoming requests.
It really is analogous to UK users going to a foreign country, buying something that their home country has an issue with, having a third party ship it to their home country, and then their home country getting mad at the store.
NZ agreed to cooperate with the US request. That made all the difference. If the US agrees to allow UK to proceed, then that's trouble for 4chan.
How exactly do they do that? Do they have peering agreements with UK-based ISPs?
I'll concede that it's not terribly far fetched. If the french entity produced a good that is illegal in the UK put it in the post to be delivered to the UK, then we have something like an analog to producing HTML in one place and displaying elsewhere.
However, the thing about sovereignty is that you don't have it if you can't enforce it.