Functional magnetic resonance imaging (fMRI) has greatly advanced our understanding of neurodevelopment. However, head motion during fMRI acquisition remains a significant challenge, especially for pediatric subjects. Excessive head motion can introduce substantial artifacts into fMRI scans, degrading the accuracy of subsequent analyses. Although motion correction methods have been proposed to directly eliminate motion effects from fMRI signals, the resulting functional connectivity (FC), the key component in fMRI studies, still contains substantial motion-induced artifacts. Effective motion correction methods applicable to FC are therefore highly desirable but remain unexplored. To address this gap, given the complementary information provided by different brain atlas parcellation schemes, we propose a novel Multi-Atlas Representation Alignment Transformer (MARA-Former) for joint motion correction of FCs derived from multiple atlases by leveraging their intrinsic relationship. Specifically, (1) we develop an FC-specified conditional Transformer architecture. By conditioning our model on both the input high-motion degree and the target low-motion degree, it can adaptively extract motion-aware features and generate low-motion results, thereby enhancing its ability in handling different motion degrees. (2) We employ optimal transport to align the representations of different atlases and design an atlas fusion block to enable comprehensive information exchange and joint learning across atlases, thereby effectively integrating complementary information and intrinsic relationships across atlases to jointly correct multi-atlas high-motion FCs. Extensive experiments on 1,289 resting-state fMRI scans of infants demonstrate the superiority of our MARA-Former in generating low-motion FCs from varying high-motion inputs. Moreover, downstream experiments further validate its effectiveness in FC-based infant brain development analysis.