The comprehensive theoretical study is performed to determine the best proximity potentials in reproducing 6,8He + 65Cu fusion reactions. Twenty three different versions of proximity potentials that consist of Prox 66, Prox 76, Prox 77, Prox 79, Prox 81-I, Prox 81-II, Prox 81-III, Prox 84, Prox 88, Mod-Prox-88, Prox 95, Prox 2003-I, Prox 2003-II, Prox 2003-III, Prox 2010, BW 91, AW 95, Bass 73, Bass 77, Bass 80, CW 76, Ngo 80, and D are used. The theoretical results are compared with experimental data on 6,8He + 65Cu fusion reactions. The appropriate proximity potentials are determined.