Image demoiréing remains a challenging task due to the complex interplay between texture corruption and color distortions caused by moiré patterns. Existing methods, especially those relying on direct image-to-image restoration, often fail to disentangle these intertwined artifacts effectively. While wavelet-based frequency-aware approaches offer a promising direction, their potential remains underexplored. In this paper, we present Freqformer, a Transformer-based framework specifically designed for image demoiréing through targeted frequency separation. Our method performs an effective frequency decomposition that explicitly splits moiré patterns into high-frequency spatially-localized textures and low-frequency scale-robust color distortions, which are then handled by a dual-branch architecture tailored to their distinct characteristics. We further propose a learnable Frequency Composition Transform (FCT) module to adaptively fuse the frequency-specific outputs, enabling consistent and high-fidelity reconstruction. To better aggregate the spatial dependencies and the inter-channel complementary information, we introduce a Spatial-Aware Channel Attention (SA-CA) module that refines moiré-sensitive regions without incurring high computational cost. Extensive experiments on various demoiréing benchmarks demonstrate that Freqformer achieves state-of-the-art performance with a compact model size. The code is publicly available at https://github.com/xyLiu339/Freqformer.