We describe the cavity-enhancement of frequency combs over a wide tuning range of 450-700 nm (> 7900 cm$^{-1}$), covering nearly the entire visible spectrum. Tunable visible frequency combs from a synchronously-pumped optical parametric oscillator are coupled into a 4-mirror, dispersion-managed cavity with a finesse of 600 to 1400. An intracavity absorption path length enhancement greater than 190 is obtained over the entire tuning range, while preserving intracavity spectral bandwidths capable of supporting sub-200 fs pulse durations. These tunable cavity-enhanced frequency combs can find many applications in nonlinear optics and spectroscopy.