We present a comprehensive study of the temperature- and magnetic-field-dependent magnetization, specific heat, and local crystal structure across the first-order ferromagnetic-paramagnetic transition in Eu₂In. Anomalies in the magnetocaloric response are observed near H ≈ 25~kOe, including changes in field scaling of magnetic entropy, local entropy exponent, and universal master curve, which suggest an apparent weakening of the first-order character of the transition. However, quantitative analysis of the magnetocaloric parameters together with modified Arrott plots demonstrates that the transition remains first order up to at least 70 kOe. Specific-heat measurements reveal a field-induced splitting of the sharp zero-field anomaly into a doublet, providing a natural explanation for the change in the magnetocaloric response. Magnetic field dependent extended x-ray absorption fine structure (EXAFS) measurements show no detectable field-induced changes in the local coordination environment of Eu. We therefore attribute these observations to a magnetic field induced two-step transition process in Eu₂In.