Text line localization in document images is still considered an open research task. The state-of-the-art methods in this regard that are only based on the classical image analysis techniques mostly have unsatisfactory performances especially when the document images i) contain significant degradations and different noise types and scanning defects, and ii) have touching and/or multi-skewed text lines or overlapping words/characters and non-uniform inter-line space. Moreover, localizing text in ancient handwritten Arabic document images is even more complex due to the morphological particularities related to the Arabic script. Thus, in this paper, we propose a hybrid method combining a deep network with classical document image analysis techniques for text line localization in ancient handwritten Arabic document images. The proposed method is firstly based on using the U-Net architecture to extract the main area covering the text core. Then, a modified RLSA combined with topological structural analysis are applied to localize whole text lines (including the ascender and descender components). To analyze the performance of the proposed method, a set of experiments has been conducted on many recent public and private datasets, and a thorough experimental evaluation has been carried out.