AbstractX-ray sources have a strong social impact, being implemented for biomedical research, material and environmental sciences. Nowadays, compact and accessible sources are made using lasers. We report evidence of nontrivial spectral-angular correlations in a laser-driven betatron X-ray source. Furthermore, by angularly-resolved spectral measurements, we detect the signature of spatial phase modulations by the electron trajectories. This allows the lateral coherence function to be retrieved, leading to the evaluation of the coherence area of the source, determining its brightness. Finally, the proposed methodology allows the unprecedented reconstruction of the size of the X-ray source and the electron beam emittance in the two main emission planes in a single shot. This information will be of fundamental interest for user applications of new radiation sources.