Context. Observations of the phase curves and secondary eclipses of extrasolar planets provide a window onto the composition and thermal structure of the planetary atmospheres. For example, the photometric observations of secondary eclipses lead to the measurement of the planetary geometric albedo, A_g, which is an indicator of the presence of clouds in the atmosphere. Aims. In this work, we aim to measure the A_g in the optical domain of WASP-43b, a moderately irradiated giant planet with an equilibrium temperature of ~1400 K. Methods. For this purpose, we analyzed the secondary eclipse light curves collected by CHEOPS together with TESS along with observations of the system and the publicly available photometry obtained with HST WFC3/UVIS. We also analyzed the archival infrared observations of the eclipses and retrieve the thermal emission spectrum of the planet. By extrapolating the thermal spectrum to the optical bands, we corrected for the optical eclipses for thermal emission and derived the optical A_g. Results. The fit of the optical data leads to a marginal detection of the phase-curve signal, characterized by an amplitude of 160 ± 60 ppm and 80₋₅₀⁺⁶⁰ ppm in the CHEOPS and TESS passbands, respectively, with an eastward phase shift of ~50° (1.5σ detection). The analysis of the infrared data suggests a non-inverted thermal profile and solar-like metallicity. The combination of the optical and infrared analyses allows us to derive an upper limit for the optical albedo of A_g< 0.087, with a confidence of 99.9%. Conclusions. Our analysis of the atmosphere of WASP-43b places this planet in the sample of irradiated hot Jupiters, with monotonic temperature-pressure profile and no indication of condensation of reflective clouds on the planetary dayside.