Zn(s) <==> Zn(2+) + 2e(-) E0 = 0.76 V
Cu(2+) +2e(-) <==> Cu(s) E0 = 0.34 V
Zn(s) + Cu(2+) <==> Zn(2+) + Cu(s) E0 = 1.10V

E is greater than zero, so at standard conditions this would be a spontaneous reaction.