A generalized Nash equilibrium (GNE) framework is introduced for a graphon mean field game of controls (GMFGC). Each agent's drift, cost, and hard control constraints depend on local and graphon-weighted moments of the joint state-control laws. Uniform linear independence constraint qualification and strong convexity yield stable feasible sets and a Lipschitz constrained best response. The associated GMFGC Hamilton-Jacobi-Bellman equation has a classical solution and the GMFGC Fokker-Planck-Kolmogorov equation a generalized energy solution; under weak coupling, the resulting GNE is unique. Furthermore, the \(\epsilon\)-Nash property is established for finite-network, finite-population constrained GMFGC systems.