The Giant Radio Array for Neutrino Detection (GRAND) aims to detect radio signals from extensive air showers (EAS) caused by ultra-high-energy (UHE) cosmic particles. Galactic, hardware-like, and anthropogenic noise are expected to contaminate these signals. To address this problem, we propose training a supervised convolutional network known as an encoder-decoder. This network is used to learn a coded representation of the data and remove specific features from it. This denoiser is trained using high-fidelity air shower simulations specifically tailored to replicate the characteristics of signals detected by GRAND. In this contribution, we describe our machine-learning model and report initial results demonstrating the sensitivity enhancement resulting from our denoising algorithm when applied to realistically simulated GRAND signals with varying signal-to-noise ratios.