Political economy models often assume that voter beliefs are consistent with available information. Recent work emphasizes instead the role played by narratives, subjective causal models that may be incorrectly specified. In this paper, we study the role of political narratives in the context of climate policy. We develop a theory of narrative entanglement, where policy dimensions—initially distinct—become strategically intertwined through narratives created by politicians to sway support. Shocks in one dimension can thus influence unrelated policy areas. We test this theory in the context of EU climate policy before versus after Russia’s invasion of Ukraine, which affected the economic costs of climate policy but not its ability to address climate change. Using a large language model to analyze speeches in the EU Parliament, we find that narratives are strongly entangled: Members of the European Parliament that emphasize the need to address climate change also emphasize economic benefits, while those denying climate change stress economic costs. After the energy price shock associated with the invasion of Ukraine by Russia, narratives shift not only in the economic dimension but also in the climate dimension, with speeches becoming less likely to imply that climate policy is necessary to combat climate change. This pattern holds at the individual politician level, with politicians from right-wing parties showing a more pronounced narrative change than those from the left.