Electron pulse trains with sub-femtosecond spike length offer novel possibilities to ultra-fast pump-probe experiments in free-electron lasers. The pulse train can be generated by an energy modulation which is converted to temporal bunching in a magnetic chicane. The source of the energy modulation is typically a resonant interaction with a co-propagating laser in a wiggler magnet. Alternatively, the modulation can be obtained by a dielectric laser accelerator (DLA). The implementation of the DLA modulation scheme at SwissFEL would be enabled by using the experimental chamber installed in the framework of the Accelerator-on-a-Chip International Program (ACHIP) and a magnetic chicane placed afterwards. In this contribution, we will focus on electron beam diagnostics for the DLA-modulated and compressed electron bunch train. Our simulation results predict that measuring the energy spread of the modulated beam and coherent diffraction radiation emitted from a foil with a hole provides a precise tool to characterize and optimize the laser-electron modulation. An absolute measurement of the longitudinal phase-space with a temporal rms-resolution of 350 as is possible with the planned X-band transverse deflecting cavity in Athos.