The CMS experiment at the Large Hadron Collider operates at the energy frontier, with a broad research programme searching for evidence of new massive particles predicted in extensions of the standard model (SM). However, if these new states are beyond the direct energy reach of the LHC, a different approach is needed. Using the framework of effective field theory (EFT), it is possible to systematically study how new physics leads to deviations from SM predictions in the energy regime accessible. The EFT introduces a set of higher dimensional operators to the SM Lagrangian that parameterise all possible beyond-the-SM interactions. The goal of the project is to study how measurements from the LHC (probing high energies) and the proposed FCC (for electroweak precision) can be combined in a global EFT fit, to provide complementary sensitivity to a wider range of beyond-the-SM effects than either could alone. Emphasis will be on mapping EFT constraints to specific beyond-the-SM theories, e.g. supersymmetry, to understand how our indirect constraints with the EFT compare with direct searches for new heavy particles.