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The foggy environment negatively affects car-following behavior, increasing rear-end collisions and energy consumption (including fuel consumption and traffic emissions). With advancements in technologies, connected automated vehicles (CAVs) are gradually replacing human-driven vehicles (HDVs) and becoming an integral part of transportation systems. The advent of CAVs offers a new approach to reducing car-following risks and energy consumption in foggy conditions. This study develops a fog-adaptive control framework for CAVs in foggy weather to mitigate car-following risks and reduce energy consumption. First, a foggy-weather car-following model, calibrated using driving simulator data, was selected to describe the behavior of HDVs in foggy highway conditions. Then, based on the model predictive control (MPC) theory, a CAV control strategy was proposed to minimize car-following risks and energy consumption in foggy weather. Finally, a simulation-based verification paradigm was established to assess objectives of risk reduction and energy saving under the proposed CAV strategy in mixed traffic. The results show that car-following risks and energy consumption vary under different fog densities and speed limit conditions. The proposed CAV control strategy can effectively reduce car-following risks by suppressing speed fluctuations, thereby lowering energy consumption in foggy mixed vehicular streams. At a 100% CAV penetration rate, the average reductions in various scenarios of fog density and speed limit conditions are as follows: ITC by 80.74%, DRAC by 59.44%, fuel consumption by 27.62%, CO2 emissions by 27.62%, CO emissions by 9.57%, HC emissions by 6.21%, and NOx emissions by 11.55%.