The superconductor-insulator transition (SIT) is considered an excellent example of a continuous quantum phase transition which is driven by zero-point quantum uctuations at zero temperature. The quantum critical point (QCP) is characterized by a diverging correlation length and a vanishing energy scale, a role which has been argued to be played by the amplitude (Higgs) collective mode of the superconducting order parameter. These low energy fluctuations near quantum criticality could be experimentally detected by specific heat measurements. Here, we use a unique highly sensitive experimental setup to measure the specific heat Cp of two-dimensional granular Pb films through the SIT. The specific heat shows the usual jump at the bulk (or “mean field”) superconducting transition temperature marking the second order phase transition. As the film thickness is tuned toward the SIT, superconducting transition temperature is relatively unchanged, while the magnitude of the jump and low temperature specific heat increase signicantly. This behaviour indicates electronic mass enhancement due to quantum fluctuations reminiscent of the effect seen in metallic magnetic to paramagnetic quantum phase transitions.