Collinear laser spectroscopy is performed on the _{30}^{79}Zn_{49} isotope at ISOLDE-CERN. The existence of a long-lived isomer with a few hundred milliseconds half-life is confirmed, and the nuclear spins and moments of the ground and isomeric states in ^{79}Zn as well as the isomer shift are measured. From the observed hyperfine structures, spins I=9/2 and I=1/2 are firmly assigned to the ground and isomeric states. The magnetic moment μ (^{79}Zn)=-1.1866(10)μ_{N}, confirms the spin-parity 9/2^{+} with a νg_{9/2}^{-1} shell-model configuration, in excellent agreement with the prediction from large scale shell-model theories. The magnetic moment μ (^{79m}Zn)=-1.0180(12)μ_{N} supports a positive parity for the isomer, with a wave function dominated by a 2h-1p neutron excitation across the N=50 shell gap. The large isomer shift reveals an increase of the intruder isomer mean square charge radius with respect to that of the ground state, δ⟨r_{c}^{2}⟩^{79,79m}=+0.204(6) fm^{2}, providing first evidence of shape coexistence.