Ecological network optimization can enhance ecological connectivity, regional ecological stability, and carbon sink capacity. Current research on ecological networks employs single-perspective optimization, which overlooks the synergistic requirements between network topological characteristics and the dual carbon goals. It lacks a comprehensive, systemic optimization framework. Focusing on the Beijing–Tianjin–Hebei region, the work constructs an ecological network by integrating ecosystem services, morphological spatial pattern analysis (MSPA), and circuit theory. A framework integrating barrier removal, structural robustness, and carbon sink enhancement is proposed, incorporating ecological barrier identification, complex network theory, and carbon offset patterns for multi-objective structural and functional optimization. The optimized network is evaluated using structural metrics, robustness analysis, and carbon sequestration validation. The network comprises 41 ecological sources and 102 corridors, exhibiting a dense northwest and sparse southeast distribution. Ecological barriers totaling 565.56 km² are removed to improve connectivity in the region. An edge-addition strategy introduces 12 nodes and 49 edges, enhancing connectivity, stability, and carbon sink capacity. Restoration priorities are set with the phased objectives of removing barriers, connecting topological weak points, and optimizing low-value carbon offset areas. Shifting the focus from structural connectivity to integrated function, the work contributes a methodological framework for advancing ecological security and carbon neutrality in urban agglomerations.