In frequency division duplex (FDD) systems, acquiring channel state information (CSI) at the base station (BS) traditionally relies on limited feedback from mobile terminals (MTs). However, the accuracy of channel reconstruction from feedback CSI is inherently constrained by the rate-distortion trade-off. To overcome this limitation, we propose a multi-modal channel reconstruction framework that leverages auxiliary data, such as RGB images or uplink CSI, collected at the BS. By integrating contextual information from these modalities, the framework mitigates CSI distortions caused by noise, compression, and quantization. At its core, the framework utilizes an autoencoder network capable of generating variable-length CSI, tailored for rate-adaptive multi-modal channel reconstruction. By augmenting the foundational autoencoder network using a transfer learning-based multi-modal fusion strategy, we enable accurate channel reconstruction in both single-modal and multi-modal scenarios. To train and evaluate the network under diverse and realistic wireless conditions, we construct a synthetic dataset that pairs wireless channel data with sensor data through 3D modeling and ray tracing. Simulation results demonstrate that the proposed framework achieves near-optimal beamforming gains in 5G New Radio (5G NR)-compliant scenarios, highlighting the potential of sensor data integration to improve CSI reconstruction accuracy.