Regarding a phase-only Fourier hologram, coherent illumination is required in its optical reconstruction. However, this requirement faces a challenge in lensless Fourier-transform correlated imaging with thermal sources. In this research, a correlated reconstruction scheme for the phase-only Fourier hologram with spatially incoherent illumination by utilizing intensity fluctuation correlation measurements is proposed. Numerical simulation and optical experiments were conducted to verify the feasibility of the correlated reconstruction scheme. Because the proposal requires neither a coherent light source nor a lens, holographic reconstruction can circumvent the limitation of the spatial coherence light source and the influence of lens aberrations.