In this paper, a novel micro combined cooling, heating, and power (MCCHP) system based on Proton Exchange (PEM) fuel cell and single-effect lithium LiBr—H2O absorption machine, was designed and studied. PEMFC exhaust gas is used for heating the building and combustor exhaust gas energy is provided to absorption chiller for house cooling. A developed mathematical model is used to predict the MCCHP unit annual energy performance and saving. The study is focused on the MCCHP unit integrated on a single-family house located into eight different French climatic cities (Trappes, Rennes, Nantes, Strasbourg, Clermont-Ferrand, Bordeaux, Orange, and Marseille). Three operational strategies: following electric load (FEL), following thermal load (FTL) and following thermal and cold loads (FTCL) are investigated. The advantage of each strategy is analysed basing on different operational parameters such as electrical, thermal and total efficiencies of the combined PEMFC-absorption chiller, hydrogen consumption, and self-consumption ratios. The proposed MCCHP has been compared with the conventional separated energy systems using the fuel energy saving ratio as a performance index. The results show that the MCCHP unit saves energy during the whole year respecting the French climatic constraints and the house energy need. The best operational strategy is for MCCHP respecting electricity demand where the yearly average fuel energy saving ratio is about 35%. Furthermore, the analyses show that the maximum Fuel Energy Saving Ratio is about 35%, obtained for a single-family house located at Marseille, while the minimum Fuel Energy Saving Ratio, about 32%, is reached for a house situated at Rennes.