Room impulse responses (RIRs) are essential for many acoustic signal processing tasks, yet measuring them densely across space is often impractical. In this work, we propose RIR-Former, a grid-free, one-step feed-forward model for RIR reconstruction. By introducing a sinusoidal encoding module into a transformer backbone, our method effectively incorporates microphone position information, enabling interpolation at arbitrary array locations. Furthermore, a segmented multi-branch decoder is designed to separately handle early reflections and late reverberation, improving reconstruction across the entire RIR. Experiments on diverse simulated acoustic environments demonstrate that RIR-Former consistently outperforms state-of-the-art baselines in terms of normalized mean square error (NMSE) and cosine distance (CD), under varying missing rates and array configurations. These results highlight the potential of our approach for practical deployment and motivate future work on scaling from randomly spaced linear arrays to complex array geometries, dynamic acoustic scenes, and real-world environments.