Binary systems of Population III can evolve to microquasars when one of the stars collapses into a black hole. When the compact object accretes matter at a rate greater than the Eddington rate, powerful jets and winds driven by strong radiation pressure should form. We investigate the structure of the jet-wind system for a model of Population III microquasar on scales beyond the jet-wind formation region. Using relativistic hydrodynamic simulations we find that the ratio of kinetic power between the jet and the disk wind determines the configuration of the system. When the power is dominated by the wind, the jet fills a narrow channel, collimated by the dense outflow. When the jet dominates the power of the system, part of its energy is diverted turning the wind into a quasi-equatorial flow, while the jet widens. From the results of our simulations, we implement semi-analytical calculations of the impact of the quasi-equatorial wind on scales of the order of the size of the binary system. Our results indicate that Population III microquasars might inject gamma rays and relativistic particles into the early intergalactic medium, contributing to its reionization at large distances from the binary system.