We have measured the upper critical field Hc2(θ) for extreme type-II granular aluminum films much thicker than the coherence length and have found them to display a strong temperature-dependent anisotropy . The temperature dependence of the parallel critical field, H(T), shows an infinite slope near Tc, which we interpret as an indication that these films have a layered structure. The perpendicular critical field, H(T), has an upward curvature, reminiscent of the behavior observed in (SN)x and some layered compounds. As a result, the anisotropy ratio decreases strongly as the temperature is lowered. We interpret this behavior as a transition towards zero dimensionality (decoupled grains). We have also measured the fluctuation conductivity σs above Tc. We find that, for films with high values of normal-state resistivity, σs follows a power law characteristic of zero dimensionality far above Tc, and characteristic of two dimensionality closer to Tc, in agreement with the proposed interpretation of the critical-field data.