The temperature dependence of the upper critical field of superconducting granular aluminum has been measured for films approaching the metal to insulator transition, down to 50 mK. The results show a progressive transition from an orbital limited critical field in the BCS side to a Pauli limited critical field close to a possible BCS-BEC crossover regime. Their ratio is in agreement with recent theoretical predictions for the behavior of the gap and of the coherence length in a Bardeen-Cooper-Schrieffer/Bose-Einstein condensate (BCS-BEC) crossover region, associated with strong coupling effects.