Photoacoustic tomography (PAT) is a promising imaging technique that can visualize the distribution of chromophores within biological tissue. However, the accuracy of PAT imaging is compromised by light fluence (LF), which hinders the quantification of light absorbers. Currently, model-based iterative methods are used for LF correction, but they require extensive computational resources due to repeated LF estimation based on differential light transport models. To improve LF correction efficiency, we propose to use Fourier neural operator (FNO), a neural network specially designed for estimating partial differential equations, to learn the forward projection of light transport in PAT. Trained using paired finite-element-based LF simulation data, our FNO model replaces the traditional computational heavy LF estimator during iterative correction, such that the correction procedure is considerably accelerated. Simulation and experimental results demonstrate that our method achieves comparable LF correction quality to traditional iterative methods while reducing the correction time by over 30 times.