Cell-free massive MIMO system is a promising technology of 5G wireless communications that provide a user-centric coverage to the user by the basestation cooperation. Most prior works on the cell-free massive MIMO systems assume the time division duplexing (TDD) systems, although the frequency division duplexing (FDD) systems dominate the current wireless communications. In the FDD systems, CSI acquisition and feedback overhead are serious concerns when the number of antennas is large. To address these problems, we use the property that the uplink and downlink multipath components are similar, so-called angle reciprocity. By exploiting the angle reciprocity, basestation can directly acquire multipath component information from the uplink pilot signal. In this paper, we propose multipath component estimation technique and basestation cooperation scheme based on the multipath components for the FDD-based cell-free massive MIMO systems. Simulation results show that the proposed multipath component estimation technique outperforms the conventional subspace-based technique. Also, we show that the FDD-based cell-free massive MIMO systems substantially improve energy efficiency over the cellular systems.