Residential buildings account for a substantial share of global energy consumption and carbon emissions. This study proposes a climate-responsive multi-objective optimisation framework for identifying optimal low-carbon residential building designs across eight representative climate zones in Central Africa. The framework combines EnergyPlus building energy simulations with the Non-dominated Sorting Genetic Algorithm II to simultaneously minimise energy consumption, initial investment cost, and operational carbon emissions while satisfying comfort constraints. To further evaluate the economic viability of the optimised solutions, carbon tax and public subsidy scenarios were introduced. The optimised sustainable configurations achieved energy savings of 53.13–59.85% relative to the reference buildings, while photovoltaic integration enabled net-negative operational carbon emissions across all climate zones. The resulting solutions required initial investments of 233.90–295.01 USD/m2, generated life-cycle benefits (LCB) of 28.45–54.81 USD/m2, achieved levelized cost of electricity (LCOE) of 0.06–0.10 USD/kWh, and exhibited payback periods (PBP) of 14–18 years. Under public subsidy scenarios, LCB increased substantially, LCOE decreased to 0.03–0.05 USD/kWh, and PBP was reduced to 6–9 years. These findings demonstrate that integrating climate-responsive design optimisation with policy-based economic incentives provides an effective decision-support framework for balancing energy efficiency, affordability, and carbon mitigation, offering practical guidance for low-carbon residential development in Central Africa.