Cell-free system where a group of base stations (BSs) cooperatively serves users has received much attention as a promising technology for the future wireless systems. In order to maximize the cooperation gain in the cell-free systems, acquisition of downlink channel state information (CSI) at the BSs is crucial. While this task is relatively easy for the time division duplexing (TDD) systems due to the channel reciprocity, it is not easy for the frequency division duplexing (FDD) systems due to the CSI feedback overhead. This issue is even more pronounced in the cell-free systems since the user needs to feed back the CSIs of multiple BSs. In this paper, we propose a novel feedback reduction technique for the FDD-based cell-free systems. Key feature of the proposed technique is to choose a few dominating paths and then feed back the path gain information (PGI) of the chosen paths. By exploiting the property that the angles of departure (AoDs) are quite similar in the uplink and downlink channels (this property is referred to as angle reciprocity), the BSs obtain the AoDs directly from the uplink pilot signal. From the extensive simulations, we observe that the proposed technique can achieve more than 80% of feedback overhead reduction over the conventional CSI feedback scheme.