Practical distributed deployments inherently suffer from asynchronous signal arrivals, which exacerbate multi-user interference and degrade system performance, especially for coherent transmission. To natively mitigate the asynchronous reception effect, this paper proposes integrating fluid antenna systems (FASs) into distributed cell-free massive MIMO systems, exploiting their reconfigurable spatial positions to release additional spatial degrees of freedom (DoFs). We establish the FAS-enabled data transmission model with asynchronous reception, i.e., delay phases. We also derive the analytical downlink spectral efficiency (SE) performance of the proposed system under coherent and non-coherent transmissions, using low-complexity Maximum Ratio (MR) precoding to provide fundamental theoretical bounds. Specifically, we propose a novel nonmonotone accelerated projected gradient ascent algorithm to jointly optimize FAS positions and power control coefficients, maximizing the downlink sum SE. Numerical results demonstrate that while asynchronous reception severely degrades system performance for coherent transmission, the spatial DoFs unlocked by optimized FAS positions, along with efficient power control, can significantly counteract the effects of unknown delay phases and outperform traditional fixed-position antennas. For non-coherent transmission, which inherently bypasses asynchronous reception, the application of FAS leverages spatial reconfigurability to natively maximize signal strength and achieve more pronounced SE gains. Ultimately, our proposed FAS-enabled system, coupled with efficient power control, mitigates performance degradation due to asynchronous reception and outperforms traditional fixed-position antennas, paving the way for the practical deployment of FASs in robust, highly efficient 6G cell-free massive MIMO systems.