This paper explores the analytical solutions for black holes in the F(R)-ModMax theory, a nonlinear electrodynamics model. The authors derive exact solutions by coupling ModMax nonlinear electrodynamics with F(R) gravity, a modified theory of gravity that can describe various astrophysical phenomena. They analyze the effects of system parameters on the event horizons and investigate the thermodynamic properties of these black holes, including Hawking temperature, electric charge, electric potential, entropy, and total mass. The first law of thermodynamics is evaluated, and the impact of various parameters on both local and global stability is examined using heat capacity and Helmholtz free energy. Finally, the thermodynamic geometry of the black hole is studied using the Hendi–Panahiyan–Eslam Panah–Momennia thermodynamic metric (HEPM's metric). The results show that the obtained solutions can be associated with black hole solutions in the F(R)-ModMax theory, and the black holes exhibit both local and global stability under certain conditions. The study also highlights the importance of the ModMax parameter in affecting the thermodynamic properties and stability of the black holes.This paper explores the analytical solutions for black holes in the F(R)-ModMax theory, a nonlinear electrodynamics model. The authors derive exact solutions by coupling ModMax nonlinear electrodynamics with F(R) gravity, a modified theory of gravity that can describe various astrophysical phenomena. They analyze the effects of system parameters on the event horizons and investigate the thermodynamic properties of these black holes, including Hawking temperature, electric charge, electric potential, entropy, and total mass. The first law of thermodynamics is evaluated, and the impact of various parameters on both local and global stability is examined using heat capacity and Helmholtz free energy. Finally, the thermodynamic geometry of the black hole is studied using the Hendi–Panahiyan–Eslam Panah–Momennia thermodynamic metric (HEPM's metric). The results show that the obtained solutions can be associated with black hole solutions in the F(R)-ModMax theory, and the black holes exhibit both local and global stability under certain conditions. The study also highlights the importance of the ModMax parameter in affecting the thermodynamic properties and stability of the black holes.