A matrix for a thermostructural fibrous composite material obtained by geopolymer synthesis based on nanocrystalline cristobalite resulting from the crystallization of geopolymer micelles of potassium polysiloxonate K—(Si—O—Si—O)n. The nanocrystalline cristobalite is in the form of micelles and/or microspheres having dimensions of less than 1 micron, preferably of less than 500 nanometers, connected together by an amorphous phase. The matrix contains at least 85 percent by weight of oxide SiO2 with at most 15%, preferably at most 10%, by weight of alkali metal oxide K2O. The nanocrystalline cristobalite results from the crystallization of geopolymer micelles of potassium polysiloxonate by a heat treatment at a temperature preferably between 600° C. and 800° C., for a time of less than 30 minutes. The fibrous composite material impregnated with this matrix is thermostructural.