The aim of the present paper is to provide a comprehensive analysis of coupling losses in perfluorinated (PF) multi-core polymer optical fibers (MC-POFs), which consist of groups of 127 graded-index cores. In our analysis we take into account geometrical, longitudinal, transverse, and angular misalignments. We perform several experimental measurements and computer simulations in order to calculate the coupling losses for a PF MC-POF prototype. Based on these results, we propose several hints of practical interest to the manufacturer which would allow an appropriate connector design in order to handle conveniently the coupling losses incurred when connectorizing two PF MC-POFs.