In power systems, flexibility can be defined as the ability to adapt to variability and uncertainty in demand and generation. Various ongoing changes in the power system are impacting the need for flexibility. We propose a novel methodology to (i) evaluate annual, weekly and daily flexibility requirements through a set of frequency spectrum analysis based metrics, (ii) examine the sensitivity of these flexibility requirements to five variables: the degree of network interconnection and the penetration of wind power, solar power, electric heating and cooling. The proposed methodology is validated on a case study focusing on the French power system, while accounting for its electrically connected neighbours. We provide an estimation of how flexibility requirements are likely to evolve in years to come; the use of global sensitivity analysis allows the identification of the variables responsible for these evolutions. The presented methodology and results can be used to identify future challenges, to evaluate the market potential of flexibility solutions and to assess the implications of policy decisions.