Berry curvature and quantum metric of Bloch states govern a wide range of phenomena, yet unified experimental access to both remains limited. Here we show that light spatial-dispersion alters the selection rules of second-order photocurrents and responses forbidden by parity become allowed in centrosymmetric crystals without any external fields, magnetic order, interfaces, strain, or engineered symmetry breaking. The resulting response is intrinsic and its weight is set by the quantum geometry of the Bloch states. Conventional photogalvanic effects are constrained by crystal symmetry and entangle the quantum metric with shift vector contributions. The spatially-dispersive response instead isolates the quantum metric and Berry curvature in distinct polarization channels. Implementing this approach in 1T'-MoTe2 across its temperature-driven transition to Td-Weyl phase, we resolve helicity-even and helicity-odd photocurrents corresponding to quantum metric and Berry curvature contributions, respectively, from the same device. The metric-dominated response persists across both phases and exhibits a robust spectral structure reproduced by first-principles calculations and linked to momentum-resolved quantum metric hotspots. In contrast, the curvature-driven channel emerges only when inversion symmetry is broken and shows strong sensitivity to carrier doping through competing momentum-space contributions. Our results establish photogalvanic effects with spatially varying optical fields as a general route to accessing quantum geometry in materials where photon energy and electronic filling probe different parts of the excitation manifold.