Supersonically cooled discharge radical atom sources are combined with high-sensitivity IR absorption methods to investigate state-to-state reactive scattering of F + n-H-2 --> HF(upsilon, J) + H in low-density crossed supersonic jets at center-of-mass collision energies of 2.4(6) kcal/mole. The product HF(upsilon, J) is probed with full vibrational and rotational quantum state selectivity via direct absorption of a single mode (Delta nu approximate to 0.0001 cm(-1)), tunable F-center laser in the Delta upsilon = 1 fundamental manifold with near shot noise limited detection levels of 10(8) molecules/cm(3)/quantum state per pulse. The high absorption sensitivity, long mean free path lengths, and low-density conditions in the intersection region permit collision-free HF(upsilon, J) rovibrational product state distributions to be extracted for the first time. Summed over all rotational levels, the HF vibrational branching ratios are 27.0(5)%, 54.2(23)%, 18.8(32)%, and <2(2)%, respectively, into upsilon(HF) = 3:2:1:0 The nascent vibrational distributions are in good agreement with rotationally unresolved crossed-beam studies of Neumark et al. [J. Chem. Phys. 82, 3045 (1985)], as well as with full quantum close-coupled calculations of Castillo and Manolopoulos [J. Chem. Phys. 104, 6531 (1996)] on the lowest adiabatic F+H-2 potential surface of Stark and Werner [J. Chem. Phys. 104, 6515 (1996)]. At a finer level of quantum state resolution, the nascent rotational distributions match reasonably well with full quantum theoretical predictions, improving on the level of agreement between theory and experiment from early arrested relaxation studies. Nevertheless, significant discrepancies still exist between the fully quantum state-resolved experiment and theory, especially for the highest energetically allowed rotational levels.