We study S-wave interactions in the $I(J^P) = \frac{1}{2}(1^+)$ $\Lambda_cN$ - $\Sigma_cN$ system on the basis of the coupled-channel HAL QCD method. The potentials which are faithful to QCD S-matrix below the $\Sigma_c^*N$ threshold are extracted from Nambu-Bethe-Salpeter wave functions on the lattice. For the simulation, we employ the (2+1)-flavor gauge configurations on a (2.9 fm)$^3$ volume at $m_\pi \simeq 700,~570,~410$ MeV. We present our results of the S-wave coupled-channel potentials for the $\Lambda_cN$ - $\Sigma_cN$ system in the $\frac{1}{2}(1^+)$ state as well as scattering observables obtained from the extracted potential matrix. We observe that the attraction in the $\Sigma_cN$ channel is stronger than that in the $\Lambda_cN$ channel and the coupling between $\Lambda_cN$ and $\Sigma_cN$ channels is weak.