A court decision ordering Royal Dutch Shell RDS.A -0.12% PLC to cut its carbon emissions has emboldened litigants in similar cases, including two that could have big implications for Exxon Mobil Corp. XOM 0.44% and French oil giant Total.

Companies in various industries have already grasped the ruling’s potential ripple effects, such as whether they will need to speed up plans to reduce their emissions, lawyers said, and are seeking…

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