fftvis simulates radio interferometric visibilities using a Non-Uniform Fast Fourier Transform (NUFFT) for fast, accurate forward modeling. It uses FINUFFT (ascl:2412.007) to match existing tools such as matvis (ascl:2312.030) to high precision while typically improving runtimes by about an order of magnitude. The package is designed as a near drop-in replacement for matvis and exposes an extensible backend interface for adding new implementations. Its modular structure separates abstract interfaces, CPU-specific code, and a high-level wrapper that maintains backward compatibility.