Yes but they can try to avoid it linguistically.

https://www.middleeasteye.net/news/israel-netanyahu-icc-arrest-warrant-was-legal-france-italy-greece-airspace

According to Ben Saul, an international law professor and UN special rapporteur on protecting rights and freedoms while countering terrorism, the Rome Statute imposes an obligation on states parties to comply with requests for arrest and surrender of any wanted person “found” on their territory.

That guy is a UN rapporteur so he’ll say pro Western stuff. Independent experts however say:

Sergey Vasiliev, a leading expert in international criminal law, told MEE that whereas ICC member states do not have the obligation “not to allow” Netanyahu’s overflight, the interpretation of Article 89 (1) of the Rome Statute should take into account the fact that airspace is traditionally included within the notion of state territory.

“If France, Italy and Greece did not wish to put themselves in a situation where they would have to arrest Netanyahu, (potentially at the cost of aerial safety), they could avoid doing so by withholding authorisation to use their airspace and preventing the overflight,” said Vasiliev.

Vasiliev, who is a professor of international law at the Open University of the Netherlands, noted that failing to take action against Netanyahu’s overflight violates the duty to cooperate fully with the ICC’s requests, in accordance with Article 86 of the Rome Statute.

EU states have on and off banned Netanyahu from using their flight space but it’s looking like he got full clearance again.

They’re legally required to down the airplane. Or more likely deny permission from entering since planes always ask for permission to enter airspace.