Deformable image registration (DIR) is a crucial and challenging technique for aligning anatomical structures in medical images and is widely applied in diverse clinical applications. However, existing approaches often struggle to capture fine-grained local deformations and large-scale global deformations simultaneously within a unified framework. We present FractMorph, a novel 3D dual-parallel transformer-based architecture that enhances cross-image feature matching through multi-domain fractional Fourier transform (FrFT) branches. Each Fractional Cross-Attention (FCA) block applies parallel FrFTs at fractional angles of $0^\circ$, $45^\circ$, $90^\circ$, along with a log-magnitude branch, to effectively extract local, semi-global, and global features at the same time. These features are fused via cross-attention between the fixed and moving image streams. A lightweight U-Net style network then predicts a dense deformation field from the transformer-enriched features. On the intra-patient ACDC cardiac MRI dataset, FractMorph achieves state-of-the-art performance with an overall Dice Similarity Coefficient (DSC) of $86.45\%$, an average per-structure DSC of $75.15\%$, and a 95th-percentile Hausdorff distance (HD95) of $1.54~\mathrm{mm}$ on our data split. FractMorph-Light, a lightweight variant of our model with only 29.6M parameters, preserves high accuracy while halving model complexity. Furthermore, we demonstrate the generality of our approach with solid performance on a cerebral atlas-to-patient dataset. Our results demonstrate that multi-domain spectral-spatial attention in transformers can robustly and efficiently model complex non-rigid deformations in medical images using a single end-to-end network, without the need for scenario-specific tuning or hierarchical multi-scale networks. The source code is available at https://github.com/shayankebriti/FractMorph.