The potential energy surfaces (PESs) for the electronic ground state and the three lowest excited states of the H + F2 reaction have been studied by ab initio multireference singles and doubles configuration interaction (MRCI- SD) calculations. Our main focus is laid on the description of the angular dependence of the barrier region on the ground state surface. In general, except for the cases of increased symmetry, the barrier arises from avoided- crossing interactions of the two lowest 2A' states. In the collinear case it is the interaction between the two lowest Σ states which is responsible for the barrier. Due to the weak interaction of these well-separated and not even neighboring states the barrier is relatively low. For broadside approach of H onto F2 in C(2v) symmetry the avoided crossing transforms into a symmetry induced conical intersection between the lowest 2A1 and 2B1 states. With our largest calculation we obtain a height of 0.130 eV (0.078 eV including the Davidson correction) for the collinear barrier, and of 1.12 eV (0.86 eV) for the broadside barrier at the conical intersection. We also consider semiempirical PESs frequently used for simulations of the H + F2 reaction. In comparison to our MRCI-SD results, a diatomics-in-molecules PES shows a qualitatively different angular dependence of the barrier in the broadside range. The implications of the barrier topography for the interpretation of experimental findings are discussed.