I will describe a generic version of the tamely ramified geometric Langlands correspondence (GLC) in positive characteristic for GLn, generalizing the work of Bezrukavnikov-Braverman on the unramified case. Let X be a smooth projective curve over an algebraically closed field k of characteristic p > n. I will give a spectral description of the parabolic Hitchin fibration over an open dense subset of the Hitchin base, and describe a correspondence between flat connections with regular singularities on X and twisted Higgs bundles on the Frobenius twist $X^(1)$. Then I will explain how to use a twisted version of the Fourier-Mukai transform to establish the GLC.