Magnetic proximity effects (MPE) are crucial for topological quantum devices as they enable the control of boundary states between a ferromagnetic insulator and a topological insulator. The InAs/GaInSb double quantum well system, especially when combined with a superconductor and influenced by MPE, shows promise for generating topological qubits. Nonetheless, researchers still debate the exact strength of the MPE between europium sulfide (EuS) and InAs. To directly probe the MPE, this work focuses on a EuS/InAs/GaInSb heterostructure. The heterostructure is fabricated by depositing EuS onto the passivated surface of a Hall bar made from an InAs/GaInSb double quantum well, by utilizing an electron beam evaporation system. Structural analysis using reflection high-energy electron diffraction and magnetic measurements indicate that although the resulting EuS thin films are polycrystalline, they still exhibit the desired magnetic properties, making them suitable for further study of MPE phenomena. Low-temperature magnetoresistance measurements on the fabricated Hall bar reveal several key phenomena that collectively provide evidence for the MPE. Applying a positive gate voltage shifts the electron wavefunction within the InAs layer toward the EuS interface, thereby enhancing the MPE. Under a perpendicular magnetic field, the magnetoresistance exhibits an increasing slope for the odd-parity component. Additionally, a transition from positive to negative magnetoresistance near zero field is observed. When an in-plane magnetic field is applied, a gate-enhanced negative magnetoresistance emerges. Hysteretic magnetoresistance, which corresponds to the reversal of EuS magnetization, is also detected during these measurements. The resistance-temperature curve for the heterostructure shows an obvious rising trend at low temperatures. This behavior is well described by the Kondo model, indicating the presence of exchange coupling between InAs electrons and the localized magnetic moments of EuS near the interface. Such coupling is a clear indicator that the magnetic proximity effect is present in the system. These findings collectively demonstrate the existence of a gate-tunable MPE in the EuS/InAs/GaInSb heterostructure. The ability to control the MPE through gate voltage establishes this heterostructure as a promising platform for exploring proximity-induced magnetism. Furthermore, these results underscore the potential applications of such systems in the development of spin-based electronic devices and highlight their significance for future research in topological quantum computing.