This arXiv preprint (not yet peer-reviewed) uses Euclid Early Release Observations to map internal proper motions in NGC 6397, deriving kinematics for ~15,000 member stars via multi-epoch astrometry with 0.3 mas/yr precision. The analysis identifies a sharp convective-transition gap in the velocity dispersion profile, linking it directly to the hydrogen-burning shell boundary where mixing efficiency drops. This goes beyond prior HST and Gaia work by capturing wider-field dynamics at fainter magnitudes, revealing how the gap influences mass segregation and binary disruption rates missed in smaller samples. Limitations include preliminary instrument calibration and incomplete radial coverage, risking overinterpretation of outer-cluster kinematics. Cross-referenced with Baumgardt et al. N-body models and Libralato's HST studies, the findings imply convective physics must be updated in galactic chemical-evolution simulations to avoid underpredicting metal-poor star distributions.