Fourier Neural Operators (FNOs) have recently emerged as efficient surrogate models for learning solution operators of parametric partial differential equations, including incompressible fluid flows [1]. However, for vortex-dominated unsteady regimes, standard FNOs often suffer from long-term instability, poor conservation of physical invariants [2], and limited generalization across Reynolds numbers [3], particularly in canonical bluff-body flows such as the von Kármán vortex street [4]. In this work, we introduce a spectrally constrained Fourier Neural Operator (SC-FNO) that enforces physical consistency directly in Fourier space. The proposed method combines an exact divergence-free projection of the velocity field with energy-aware spectral regularization inspired by the invariants of the incompressible Navier–Stokes equations. Unlike physics-informed losses applied in physical space, the proposed constraints operate natively in the Fourier representation used by the FNO, resulting in negligible additional computational cost. We evaluate SC-FNO on two-dimensional incompressible flow past a bluff obstacle over a range of Reynolds numbers, focusing on unsteady wake dynamics governed by von Kármán vortex shedding. Performance is assessed in terms of long-term rollout stability, spectral energy distributions, vortex shedding frequency, and force coefficient statistics, and compared against standard FNO baselines. The results demonstrate that enforcing physical constraints directly in the spectral domain significantly improves stability, robustness, and physical fidelity in vortex-dominated unsteady flow prediction.