The differential cross sections and decay angular distributions for coherent φ-meson photoproduction from helium-4 are measured for the first time at forward angles with linearly polarized photons in the energy range Eγ=1.685-2.385GeV. Thanks to the target with spin-parity JP=0+, unnatural-parity exchanges are absent, 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 strong dominance (>94%) of natural-parity exchanges in this reaction. To evaluate the contribution from natural-parity exchanges to the forward cross section (θ=0â) for the γp→φp reaction near threshold, the energy dependence of the forward cross section (θ=0â) for the γHe4→φHe4 reaction is analyzed. The comparison to γp→φp 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 γp→φp reaction near threshold.