We study the ground states for a system of two coupled Hartree equations with both attractive intraspecies and attractive interspecies interactions in RN (N≥3), which can also be described by L2-constraint minimizers of mass critical Hartree energy functionals with trapping potentials. The existence and nonexistence of minimizers are classified completely by establishing the refined Gagliardo-Nirenberg type inequality. Based on some delicate estimates of the Hartree energy functional, the limit behavior of minimizers is also analyzed as the interspecies interaction strength goes to a critical value, where each component of minimizers blows up and concentrates at a flattest common minimum point of trapping potentials. An optimal blow-up rate of minimizers for the Hartree energy functional is concomitantly obtained.