Most existing Multimodal Sentiment Analysis (MSA) methods rely on holistic fusion, treating all modalities and temporal segments equally. Such strategies often introduce redundant information and obscure the decision process, limiting both robustness and interpretability. Inspired by dual-process theory, we propose FRSR (Fast Retrieval and Slow Reasoning), an interpretable framework that decomposes multimodal sentiment modeling into two cooperative pathways. The Fast Pathway acts as a lightweight evidence selector, using context-aware convolution and auxiliary supervision to retrieve a sparse set of Top-K sentiment-relevant cues from noisy multimodal inputs. Based on these cues, the Slow Pathway performs deeper cross-modal reasoning through learnable reasoning tokens, enabling hierarchical sentiment inference. By separating salient evidence retrieval from multimodal reasoning, FRSR improves interpretability while reducing computational cost. Experiments on three benchmark datasets show that FRSR achieves competitive performance, higher efficiency, stronger robustness to noise, and clearer decision transparency than existing holistic fusion methods.