It is not exceptional for most MEP from a member state to be in the opposition at the national level, particularly in contexts where it is seen as a protest vote. Turnout is usually low for European elections, so they tend to swing a bit more than national elections.
If you look at local politics and news they are all lobbying massively for it (or some people do). The reason is usually "for sake of the children". Parents in particular are heavily in favor of chat control.
You could interpret the results as the Danish government being for Chat Control, but "normal" Danish people not following the same trend
France has had really strange tendencies lately, e.g. when they arrested Telegram founder.
Only 51% of people able to vote in European elections actually vote (with 2,81% white ballot), so it’s not even a majority of electors sustaining them, despite abstention being at record low level in decades.
Elites being disconnected from people day-to-day reality and needs is a recurrent topic leaking even in the mainstream media which almost all owned by oligarchs by now.
European institutions are notoriously opaque and byzantine, which doesn’t really help with feeling represented, even before Qatar gates and the 1/4th of MEP revealed "implicated in judicial cases or scandals."
https://www.touteleurope.eu/institutions/elections-europeenn...
https://vote-blanc.org/europeennes-2024-la-repartition-par-d...
https://www.lemonde.fr/les-decodeurs/article/2024/06/10/euro...
https://www.bfmtv.com/politique/gouvernement/gerald-darmanin...
https://www.lemonde.fr/en/les-decodeurs/article/2024/02/02/o...