The differential cross sections and decay angular distributions for coherent $phi$-meson photoproduction from helium-4 have been measured for the first time at forward angles with linearly polarized photons in the energy range $E_{gamma} = text{1.685-2.385 GeV}$. Thanks to the target with spin-parity $J^{P} = 0^{+}$, unnatural-parity exchanges are prohibited, and thus natural-parity exchanges can be investigated clearly. The decay asymmetry with respect to photon polarization is shown to be very close to the maximal value. This ensures the dominance ($> 94%$) of natural-parity exchanges in this reaction. To evaluate the contribution from natural-parity exchanges to the forward cross section ($theta = 0^circ$) for the $gamma p rightarrow phi p$ reaction near the threshold, the energy dependence of the forward cross section ($theta = 0^circ$) for the $gamma {^{4}text{He}} rightarrow phi {^{4}text{He}}$ reaction was analyzed. The comparison to $gamma p rightarrow phi p$ data suggests that enhancement of the forward cross section arising from natural-parity exchanges, and/or destructive interference between natural-parity and unnatural-parity exchanges is needed in the $gamma p rightarrow phi p$ reaction near the threshold.