Remote sensing imagery is often degraded by cloud cover, causing severe information loss and hindering downstream Earth observation tasks. Although recent deep learning methods, including CNN- and Transformer-based models, have achieved promising progress in cloud removal, they mainly operate in the spatial domain and largely overlook the frequency-domain discrepancies introduced by clouds of different types and densities. This limitation restricts their ability to generalize across diverse cloud corruption scenarios. To address this issue, we propose a Frequency Interaction Cloud Removal Network (FI-CRNet), which introduces a novel Frequency-Aware Modulation (FAM) mechanism for high-fidelity cloud-free image reconstruction. The FAM module consists of two components. First, the Frequency Decomposition (FD) module explicitly separates input features into low-frequency cloud-affected components and high-frequency detail-rich components through spectral analysis, while aligning them with decoder features via cross-attention. Second, the Cross-Frequency Interaction (CFI) module adaptively integrates these components through a dual-gate weighting mechanism, including spatial and channel gates, to suppress cloud interference while enhancing structural and textural details. By jointly modeling frequency-domain cues and spatial features, FI-CRNet enables robust and adaptive reconstruction under diverse cloud conditions. Extensive experiments show that our method outperforms state-of-the-art techniques across diverse cloud scenarios.