A time-dependent close-coupling method is used to calculate, for the first time, fully differential cross sections for the complete fragmentation of helium by two photons. Surprising differences in the magnitude of the total-integral cross sections are found in comparisons with other calculations. These differences are found to be due to a core-excited resonance enhancement of the two-photon process for both single and double ionization. These calculations provide theoretical support for ground-breaking measurements expected to be obtained from free-electron laser experiments in the near future.