This paper presents an analytical solution for electrically charged black holes in the $ F(R) $-ModMax theory, which combines Modified Maxwell (ModMax) nonlinear electrodynamics with $ F(R) $ gravity. The study analyzes the effects of the theory's parameters on the event horizons of black holes and investigates their thermodynamic properties, including Hawking temperature, electric charge, electric potential, entropy, and total mass. The first law of thermodynamics for the system is evaluated, and the impacts of various parameters on both local and global stability are examined using heat capacity and Helmholtz free energy. The thermodynamic geometry of the black hole in $ F(R) $-ModMax gravity is studied using the Hendi–Panahiyan–Eslam Panah–Momennia (HPEM) thermodynamic metric. The black hole solutions in $ F(R) $-ModMax theory are derived, and the metric function is analyzed to determine the event horizons. The Kretschmann scalar is used to identify the curvature singularity at $ r = 0 $. The analysis shows that the number of horizons depends on the parameters $ R_0 $ and $ \gamma $. For $ R_0 > 0 $, there are three horizons: an inner horizon, an event horizon, and a cosmological horizon. For $ R_0 < 0 $, the solution may have two horizons, one horizon, or a naked singularity, depending on the parameters. The thermodynamic quantities of the black holes are calculated, and the first law of thermodynamics is verified. The Hawking temperature is found to depend on the electric charge, $ f_{R_0} $, and $ R_0 $. The heat capacity and Helmholtz free energy are used to analyze the local and global stability of the black holes. The results show that the black holes have a real root for the Hawking temperature, which is influenced by the parameters. The analysis of the heat capacity reveals that the black holes have physical and stable regions, with the local stability decreasing as $ \gamma $ increases. The global stability is determined by the negative value of the Helmholtz free energy, indicating that large black holes are globally stable. The thermodynamic geometry of the black hole is studied using the HPEM metric, which shows that the divergence points of the Ricci scalar coincide with both the phase transition critical points and the physical limitation points of the heat capacity. The analysis confirms that the HPEM metric effectively distinguishes between these points. The study concludes that the obtained solution in $ F(R) $-ModMax theory can be associated with the black hole solution in this theory, and the black holes have physical and stable regions depending on the parameters.This paper presents an analytical solution for electrically charged black holes in the $ F(R) $-ModMax theory, which combines Modified Maxwell (ModMax) nonlinear electrodynamics with $ F(R) $ gravity. The study analyzes the effects of the theory's parameters on the event horizons of black holes and investigates their thermodynamic properties, including Hawking temperature, electric charge, electric potential, entropy, and total mass. The first law of thermodynamics for the system is evaluated, and the impacts of various parameters on both local and global stability are examined using heat capacity and Helmholtz free energy. The thermodynamic geometry of the black hole in $ F(R) $-ModMax gravity is studied using the Hendi–Panahiyan–Eslam Panah–Momennia (HPEM) thermodynamic metric. The black hole solutions in $ F(R) $-ModMax theory are derived, and the metric function is analyzed to determine the event horizons. The Kretschmann scalar is used to identify the curvature singularity at $ r = 0 $. The analysis shows that the number of horizons depends on the parameters $ R_0 $ and $ \gamma $. For $ R_0 > 0 $, there are three horizons: an inner horizon, an event horizon, and a cosmological horizon. For $ R_0 < 0 $, the solution may have two horizons, one horizon, or a naked singularity, depending on the parameters. The thermodynamic quantities of the black holes are calculated, and the first law of thermodynamics is verified. The Hawking temperature is found to depend on the electric charge, $ f_{R_0} $, and $ R_0 $. The heat capacity and Helmholtz free energy are used to analyze the local and global stability of the black holes. The results show that the black holes have a real root for the Hawking temperature, which is influenced by the parameters. The analysis of the heat capacity reveals that the black holes have physical and stable regions, with the local stability decreasing as $ \gamma $ increases. The global stability is determined by the negative value of the Helmholtz free energy, indicating that large black holes are globally stable. The thermodynamic geometry of the black hole is studied using the HPEM metric, which shows that the divergence points of the Ricci scalar coincide with both the phase transition critical points and the physical limitation points of the heat capacity. The analysis confirms that the HPEM metric effectively distinguishes between these points. The study concludes that the obtained solution in $ F(R) $-ModMax theory can be associated with the black hole solution in this theory, and the black holes have physical and stable regions depending on the parameters.