In this paper, we jointly design linear partial zero-forcing (PZF) precoding and peak-to-average power ratio (PAPR) reduction techniques in downlink cell-free massive MIMO systems based on orthogonal frequency-division multiplexing (CF-mMIMO-OFDM). The key idea is to perform a local PAPR reduction of transmitted signals while exploiting the features of the emerging local PZF precoding scheme. Specifically, we anticipate the power amplifier (PA)-induced distortions by transmitting low-PAPR, i.e, hardware friendly, signals. Then the distortions related to PAPR reduction is controlled in the way that is precoded to be transmitted onto a space where the communication is weak, while protecting the strong communications. The joint PZF and PAPR reduction is formulated as a simple convex optimization problem solved via an efficient and steepest iterative algorithm. Interestingly, the proposed scheme is implemented in a distributed and scalable manner, demonstrating the benefits of PZF based CF -mMIMO-OFDM. The simulation results show that the proposed method holds significant promise in effectively reducing the substantial effects of non-linear distortion introduced by PAs at the access points. In addition, we provide the values of the optimal grouping thresholds that yield the highest achievable spectral efficiency.