Distributed acoustic sensing (DAS) is a rapidly growing technology for seismic acquisition, with the potential to sample rarely available wavefield components in reservoir settings. How to best use the information that DAS supplies to estimate reservoir properties is an open question. Full-waveform inversion (FWI) of DAS data, alone or in combination with geophone data, is a natural possibility to pursue. A mixed formulation must accommodate particle velocity data and 1C measurements of strain or strain rate in the direction tangent to a fiber-optic cable, which itself may take on some characteristic shape. Expecting that these amplitude and directionality properties of DAS data will impact parameter resolution in FWI, especially when incorporating finite gauge lengths, we have developed two appraisal methods. The first is an analytic description of the relationship between the spatial period and the elastic-wave sensitivity within a helical-wound fiber (which builds on a symmetry class of fibers insensitive to shear strains). The second is an extension of scattering radiation pattern analysis to DAS sensors of arbitrary geometry. We then numerically analyze the FWI response. Using 2D simulations and several simple models including the Marmousi2, we analyze the effect that shaping of the DAS fiber has on parameter estimations, by comparing inversion results derived from straight and various coiled fibers in a horizontal well. Fiber geometry is observed to have important implications for the accuracy and fidelity of DAS-FWI parameter estimates. It is also clear that the complementary features of DAS and standard geophone data impact FWI. Simultaneous inversions of surface geophone and DAS data from horizontal wells convincingly outperform inversions from either data set alone.