In response to the challenges of global warming and the development of A low-carbon economy, the integrated electricity and natural gas energy system (IEGES) is known as an important structure for future energy supply; thus, its planning and design must take low-carbon and environmental protection factors into account. Regarding carbon emissions as an optimization criterion, this paper built life-cycle carbon emission models of IEGES components. Then, taking the capacities of the energy resources, storage and conversion units of IEGES as the optimization variables, a multi-objective optimization configuration model was established considering the annual investment operation cost and the life-cycle carbon emissions. The multi-objective model was transformed into a single-objective one by an ε-constraint approach and the polynomial fitting method was employed to obtain the value of ε for obtaining uniformly distributed Pareto sets. Based on the fuzzy entropy weight method and the fuzzy affiliation degree approach, the obtained Pareto sets were ranked and the solution with the highest ranking value was selected as the optimal solution for the original problem. Finally, the configuration schemes were analyzed from the perspectives of economy, carbon emission and renewable energy utilization, and the effectiveness and rationality of the proposed optimization method were verified through MATLAB simulation.