This study presents a methodological framework for designing a hydrogen supply chain (HSC) utilizing a superstructure that incorporates various alternatives for feedstock, production, storage, transportation, and distribution. The framework features a mixed-integer non-linear mathematical model that includes innovative factors such as power efficiencies, continuous sizing capacities, and time-varying costs of different energy feedstocks related to the learning rate. Furthermore, emerging production technologies such as alkaline electrolysis and proton exchange membrane water electrolysis, along with steam methane reforming with carbon capture, utilization, and storage, are considered. To address the resulting bi-objective optimization problem that aims to minimize both total daily costs and greenhouse gas emissions, a specialized solution strategy based on bi-level decomposition and a matheuristic algorithm is developed. This methodology for designing HSCs is applied to a case study in southern France, demonstrating the effectiveness of the solution technique in approximating the Pareto frontier. By analyzing in detail selected relevant solutions along the Pareto front, insights into the spatial, temporal, and technological deployment of the HSC are gained, enabling decision-makers to make informed choices based on economic and environmental criteria.