Over time, investors have become increasingly aware of the risks associated with a transition to a low-carbon economy. This study investigates the association between carbon emissions and the cost of debt financing for a sample of firms from the eurozone in the period 2010-2018. The results provide evidence that the risk premium required by lenders increases with carbon emissions. However, although the most polluting sectors were already charged before the Paris Agreement, and not further penalised in the subsequent period, our results indicate that the less polluting sectors started being charged a higher spread for their emissions only in the period after the Agreement. The Paris Agreement appears to be a turning point around which lenders have become aware of the strong commitment taken by policymakers in fighting climate change. Our findings also suggest that increased levels of disclosure on climate-related issues can mitigate corporate carbon risk. On the other hand, the results are not compelling when we consider the effect of control mechanisms, such as external verification for emissions, board oversight of carbon risk and the presence of emission reduction targets, on the cost of debt. Taken as a whole, the results demonstrate the effectiveness of public policies in driving lenders' allocation decisions as well as the role of climate-related disclosure in mitigating the corporate cost of capital. As such, our findings have important implications for both policymaking in environmental regulation and managerial strategies.