The carbon–financial nexus helps firms evaluate susceptibility to carbon risk more effectively. This is the first research article to model the short- and long-run co-integrating association between European financial markets, the CBOE oil price volatility index (OVZ) and the European carbon emission trading system (EU-ETS) by using the daily returns from 1 October 2013 to 1 October 2023. We utilize co-integration test followed by the ARDL framework with an error correction mechanism (ECM). Moreover, we utilize the DCC-GARCH-t copula framework to estimate the hedge ratio and to select an optimal portfolio weight for carbon risk hedging. Overall, the findings suggested that EU-ETS (OVZ) has a consistent positive (negative) short-term influence on all the equity returns of Belgium, Denmark, Finland, France, Germany, Ireland, Italy, Netherlands, Spain and the stock indices of the whole Eurozone. However, in the long term, EU-ETS has a positive (negative) effect on the stock returns of France and the Eurozone (Belgium and Spain). Belgian and Spanish companies could implement long-term carbon reduction policies. Belgian and Spanish firms should focus on the utilization of green energy resources and the internalization of carbon emission-free mechanical processes as this may offer a safeguard against the additional pressure arising from escalating carbon prices. Finally, an optimal portfolio weight selection strategy based upon the DCC-GARCH-t copula approach aims for higher hedging effectiveness (HE) than the hedge ratio strategy when adopting short-term positions in Italian and Danish equity markets to reduce the risk of long-term EU-ETS volatility.