Accurate beam alignment is a critical challenge in XL-MIMO systems, especially in the near-field regime, where conventional far-field assumptions no longer hold. Although 2D grid-based codebooks in the polar domain are widely accepted for capturing near-field effects, they often suffer from high complexity and inefficiency in both time and computational resources. To address this issue, we propose a novel line-of-sight (LoS) near-field beam alignment scheme that leverages the discrete Fourier transform (DFT) matrix, which is commonly used in far-field environments. This approach ensures backward compatibility with the legacy DFT codebook for far-field signals by allowing its reuse. By introducing a new method to analyze the energy spread effect, we define the concept of an $ε$-approximated signal subspace, spanned by DFT vectors that exhibit significant correlation with the near-field channel vector. Building on this analysis, the proposed hybrid scheme integrates model-based principles with data-driven techniques. Specifically, it utilizes the properties of the DFT matrix for efficient coarse alignment while employing a deep neural network (DNN)-aided fine alignment process. The fine alignment operates within the reduced search space defined by the coarse alignment stage, significantly enhancing accuracy while reducing complexity. Simulation results demonstrate that the proposed scheme achieves superior alignment performance while reducing both computational and model complexity compared to existing methods.