With the increasing share of intermittent renewable energy sources in the energy mix, demand-side flexibility is likely to play a key role in the future. For buildings, flexibility is defined as the ability to shift their energy consumption away from “peak periods” i.e. high-demand periods of the electrical network. In France, these episodes occur mainly during the wintertime due to the significant demand for space heating. To achieve flexibility objectives, we explore an indirect control strategy at district scale by adjusting the dwelling thermostat during peak periods. The study is conducted over 337 dwellings in order to better predict the load curve by taking advantage of the aggregation effect. Three main research questions are addressed in relation to the assessment of flexibility potential: (i) the effect of aggregation, (ii) the identification of the most influencing factors, including occupant behavior, and (iii) the quantification of uncertainties. Using an urban building energy modeling tool populated with various national data sources (building envelope, energy class of equipment, etc), we perform a sensitivity analysis on 22 parameters representing the geometry, the appliances, the building characteristics, the occupants, and the grid. The output indicator is the average power shifted during the flexibility (or demand response) event. From this analysis, 7 parameters appear as being the most influential. A regression analysis on these parameters is performed, depending on both the duration of the event and the typology of district. The results show that the duration of the flexibility event and the occupant pre-selected temperature change are the most influential parameters. It results to approximately ± 90 W of uncertainty on an average potential of 290 W of shiftable power per household in a recent district. Furthermore, the occupants are highlighted as making a significant contribution to flexibility. Finally, we observed that the thermal properties investigated with the study of an old fabric district play a key role. Low thermal performance means high heating consumption and increased flexibility potential, but a similar relative uncertainty.