This work presents the EFDA Times model (ETM), developed within the European Fusion Development Agreement (EFDA). ETM is an optimization global energy model which aims at providing the optimum energy system composition in terms of social wealth and sustainability including fusion as an alternative technology in the long term. Two framework scenarios are defined: a Base case scenario with no limits to CO2 emissions, and a 450ppm scenario with a limit of 450ppm in CO2-eq concentrations set by 2100. Previous results showed that in the Base case scenario, with no measures for CO2 emission reductions, fusion does not enter the energy system. However, when CO2 emission restrictions are imposed, the global energy system composition changes completely. In a 450ppm scenario, coal technologies disappear in a few decades, being mainly replaced by nuclear fission technologies which experience a great increase when constrained only by Uranium resources exhaustion. Fission technologies are then replaced by the fusion power plants that start in 2070, with a significant contribution to the global electricity production by 2100. To conclude the work, a sensitivity analysis will be presented on some parameters that may affect the possible role of fusion in the future global energy system.