Zero-carbon energy infrastructure design has become one of the most consequential pivotal toward sustainable development. This article introduces a novel approach to energy infrastructure innovation that incorporates carbon-free energy generation resources- renewables and Micro Nuclear Reactors (MNRs). The integrated Nuclear-Renewable Microgrid (NRM) has minimal greenhouse gas emissions and the utmost reliability. However, the planning and modeling of NRMs may face challenges due to the variability and uncertainty of renewable resources. Therefore, the study proposes a probabilistic energy modeling approach for NRMs, which provides an outstanding estimation for energy system planning in terms of economics and resiliency. Multiple load-generation scenarios have been formulated based on the probability distribution functions. A recent nature-based optimization technique, Slime Mould Algorithm (SMA), is employed to minimize the total annual cost of the probabilistic model with reliability constraints. The statistical analyses reveal that the probabilistic energy modeling method perfectly evaluates how energy generation resources should be mixed to fulfill energy demand in an optimal manner. The key findings also demonstrate observations on finance, system resiliency, and system components before the commencement of the project. The results are validated by another recent metaheuristic optimization algorithm called Aquila Optimizer (AO).