Deep observations have detected extended Ly$\alpha$ emission nebulae surrounding tens of quasars at redshift 2 to 6. However, the metallicity of such extended haloes is still poorly understood. We perform a detailed analysis on a large sample of 80 quasars at $z\sim 3$ based on MUSE-VLT data. We find clear evidence of extended emission of the UV nebular lines CIV and HeII for about 18$\%$ of the sample, while CIII] is only marginally detected in a few objects. By stacking the cubes we detect emission of CIV, HeII and CIII] out to a radius of about 45 kpc. CIV and HeII show a radial decline much steeper than Ly$\alpha$, while CIII] shows a shallower profile similar to Ly$\alpha$ in the inner 45 kpc. We infer that the average metallicity of the circumgalactic gas within the central 30-50~kpc is $\sim$0.5solar,orevenhigher.However,wealsofindevidenceofacomponentoftheLy$\alpha$ haloes, which has much weaker metal emission lines relative to Ly$\alpha$. We suggest that the high metallicity of the circumgalactic medium within the central 30-50 kpc is associated with chemical pre-enrichment by past quasar-driven outflows and that there is a more extended component of the CGM that has much lower metallicity and likely associated with near-pristine gas accreted from the intergalactic medium. We show that our observational results are in good agreement with the expectations of the FABLE zoom-in cosmological simulations.