Context.Current simulations indicate that the first stars were formed predominantly in binary systems. Studying the contribution of the first accreting binary systems to the reionization and heating of the intergalactic medium requires formulating a concrete model for Population III microquasars.Aims.We aim at constructing a complete model for microquasars with a Population III donor star.Methods.We considered that the mass loss of the star is exclusively caused by the spill of matter through the Roche lobe toward the black hole. We calculated the spectral energy distribution of the radiation produced by the accretion disk, the radiation-pressure-driven wind, and the relativistic particles in the jets, within the framework of a lepto-hadronic model. In addition, we estimated the effect on the reionization by the first microquasars.Results.We determine that Population III microquasars are powerful sources of ultraviolet radiation produced by the winds of their super-critical disks, and that they generate a broadband nonthermal emission in jets.Conclusions.Our results indicate that microquasars in the early Universe could have been important for the reionization and heating of the intergalactic medium.