Graphene and 2D analogs such as transition metal dichalcogenides (TMDCs) have been widely investigated for their tuneable electronic properties. There is a large spectrum of applications of such 2D analogs; for example, non-volatile memory, which is a key building block for future low-power consumer electronics. In this work, we have investigated a vertical heterostructure composed of a chemical vapour-deposited molybdenum disulphide transistor channel coupled with silicon tunnel oxide (SiO2) and hafnium oxide as a blocking barrier, with fluorographene (FGr) being used as the charge trapping medium. Owing to the larger trap density of FGr, the memory window is three times larger, and the data retention measurements at room temperature yield a 50% charge loss extrapolated to 10 years. The low barrier at the FGr/SiO2 interface induces a steeper charge loss for holes. Nevertheless, the stack can sustain at least to 550 cycles without showing any sign of degradation. Although bandgap engineering is required to improve the data retention, particularly for the holes, the combination studied here is an encouraging route for 2D-based non-volatile memories.