In this work, we apply the recently developed frequency shift of nanoantennas (FRESA) technique to measure the Young's modulus of thin mesoporous films at GHz frequencies as a function of porosity with local precision. The method measures changes in the mechanical oscillation frequency of optically excited plasmonic nanoantennas with modification of their surrounding medium. The values obtained range from 4 to 10 GPa for porosities extending from 35 to 4%, compatible with reports on films grown under similar conditions. We further find comparable results when using the well-established nanoindentation (NI) technique, validating the new method. By analysis of the nanoresonator's quality factor, the measurement reveals an excellent interfacial adhesion of the films to the nanoantennas. Different from most other characterization techniques, FRESA provides elastic modulus determination at GHz frequencies, relevant for the operation of current devices. Furthermore, FRESA exhibits, in principle, no limitations in terms of film thickness, in contrast to the NI, which is strongly affected by the stiffness of the substrate for ultrathin films.