Optical-optical double-resonance fluorescence excitation spectra of molecular Rydberg states of CaF are reported, and states up to 45500 cm-1 above the X2SIGMA+ ground state are rotationally analyzed. The new electronic states are arranged into six ''core-penetrating'' Rydberg series by fitting their energies to the Rydberg equation using effective principal quantum numbers. The ionization potential of CaF is thereby determined to be 46998+/-5 cm-1. Spin-orbit, LAMBDA-doubling, and spin-rotation constants are determined for a subset of the observed states. Scaling relationships for each of these fine-structure effects are developed and shown to yield characteristic scaling parameters for each series. Analysis, using Ca+ atomic orbitals as a basis set for the molecular Rydberg orbitals, shows that each of the six observed molecular Rydberg series correlates with a core-penetrating Rydberg series of the Ca+ ion, and that the p approximately d mixing suggested by the spin-orbit scaling parameters of the 2PI states is consistent with that previously determined for low-lying states using a ligand-field model. The spin-orbit scaling parameter for the lone 2DELTA series is consistent with pure l = 2 character. In the lowest-lying state of each series, n approximately (n + 1) mixing is shown to account for deviations of the molecular constants from scaling predictions based on the corresponding constants of the higher-lying states. The coefficients of scaling relations for the LAMBDA-doubling and spin-rotation constants reveal interseries interactions which are consistent with substantial l mixing and which suggest that multistate perturbation and/or multichannel quantum-defect analyses should be pursued.