Geopolymer has been selected as a hydraulic mineral binder for the immobilization of MgZr fuel cladding coming from the dismantling of French Uranium Natural Graphite Gas reactor dedicated to a geological disposal. In this context, the corrosion processes and the nature of the corrosion products formed on MgZr alloy in a geopolymer matrix with and without the corrosion inhibitor NaF have been determined using a multiscale approach combining in situ Grazing Incidence hard X-ray Diffraction, Raman microspectroscopy, Scanning and Transmission Electron Microscopies coupled to Energy Dispersive X-ray Spectroscopy. The composition, the morphology, and the porous texture of the corrosion products were characterized, and the effect of the corrosion inhibitor NaF was evidenced. The results highlighted the formation of Mg(OH)$_{2−x}$F$_x$. In addition, in presence of NaF, NaMgF$_3$ forms leading to a decrease of the thickness and the porosity of the corrosion products layer. Moreover, a precipitation of magnesium silicates within the porosity of the geopolymer was evidenced. Finally, we propose a detailed set of interconnected processes occurring during the MgZr corrosion in the geopolymer.