At least in the German ruling of the constitutional court they could refere to Article 20a of the German constitution Art20a, Roughly translated: The state, in

At least in the German ruling of the constitutional court they could refere to Article 20a of the German constitution Art20a, Roughly translated: The state, in responsibility for future generations, protects the natural means of subsistence and the Animals in the constitutional order by use of legislative, excecutive and judiciary measures. Of course this doesn't say verbatim to protect the climate but I think this is enough legislative basis to rule dangerous negligence on the matter of climate change unconstitutional.