We investigate the noise transfer mechanism from the light source intensity fluctuations to the acoustic signal in Fourier transform photoacoustic spectroscopy (FT-PAS). This noise coupling is expected to be reduced in FT-PAS compared with conventional Fourier transform spectroscopy, as only the specific spectral components that are absorbed by the probed sample contribute to the noise level. We employ an incoherent supercontinuum (SC) light source in our experiments and observe a linear relation between the sample gas concentration and the detected noise level, which significantly reduces the influence of the SC noise on the detection limit. Based on our experimental results, we derive a model for the noise level, which establishes the foundation for practical sensitive implementation of FT-PAS.