Integrated sensing and communication (ISAC) systems demand precise and efficient target localization, a task challenged by rich multipath propagation in complex wireless environments. This paper introduces MARBLE-Net (Multipath-Aware Rainbow Beam Learning Network), a deep learning framework that jointly optimizes the analog beamforming parameters of a frequency-dependent rainbow beam and a neural localization network for high-accuracy position estimation. By treating the phase-shifter (PS) and true-time-delay (TTD) parameters as learnable weights, the system adaptively refines its sensing beam to exploit environment-specific multipath characteristics. A structured multi-stage training strategy is proposed to ensure stable convergence and effective end-to-end optimization. Simulation results show that MARBLE-Net outperforms both a fixed-beam deep learning baseline (RaiNet) and a traditional k-nearest neighbors (k-NN) method, reducing localization error by more than 50\% in a multipath-rich scene. Moreover, the results reveal a nuanced interaction with multipath propagation: while confined uni-directional multipath degrades accuracy, structured and directional multipath can be effectively exploited to achieve performance surpassing even line-of-sight (LoS) conditions.