I will describe a generic version of the tamely ramified geometric Langlands correspondence (GLC) in positive characteristic for $GL_n$, 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.