Demand response (DR) at the building level (also named energy flexibility) will play an important role in facilitating energy systems based mostly or entirely on renewable energy sources. Flexibility is thus deemed necessary to control the energy consumption to match the actual energy generation from various renewable energy sources such as solar and wind power. However, there is lack of comprehensive knowledge about how much energy flexibility different building types and their usage may be able to offer to the present or future energy systems. In this study, the flexibility potential of space heating is characterised among the building stock in France. Five different typologies of buildings were chosen (post-1945, BR 1982, BR 2005, BR 2012 and BR 2020) with different levels of insulation, air-tightness and thermal mass. Building energy simulations were performed, with modulations (i.e. increase or decrease) of the space heating set-point during the heating season. From this study, the large influence of the envelope properties on the flexibility potential was highlighted: the storage efficiency for upward modulations and the rebound rates for downward modulations range from 40% up to 90% in poorly insulated and well-insulated buildings, respectively. This study describes a generic method and provides quantitative data to estimate the flexibility potential for demand response at the building level and to help designing future energy grids.