Context. CONCERTO is the first experiment to perform a C II line intensity mapping (LIM) survey on the COSMOS field to target z  > 5.2. Measuring the C II angular power spectrum allows us to study the role of dusty star-forming galaxies in the star formation history during the epochs of Reionization and post-Reionization. The main obstacle to this measurement is the contamination by bright foregrounds: the dust continuum emission and atomic and molecular lines from foreground galaxies at z  ≲ 3. Aims. We evaluate our ability to retrieve the C II signal in mock observations of the sky using the Simulated Infrared Dusty Extragalactic Sky (SIDES), which covers the mid-infrared to millimetre range. We also measure the impact of field-to-field variance on the residual foreground contamination. Methods. We compared two methods for dealing with the dust continuum emission from galaxies (i.e. the cosmic infrared background fluctuations): the standard principal component analysis (PCA) and the asymmetric re-weighted penalized least-squares (arPLS) method. For line interlopers, the strategy relies on masking low-redshift galaxies using the instrumental beam profile and external catalogues. As we do not have observations of CO or deep-enough classical CO proxies (such as L IR ), we relied on the COSMOS stellar mass catalogue, which we demonstrate to be a reliable CO proxy for masking. To measure the angular power spectrum of masked data, we adapted the P of K EstimatoR (POKER) from cosmic infrared background studies and discuss its use on LIM data. Results. The arPLS method achieves a reduction in the cosmic infrared background fluctuations to a sub-dominant level of the C II power at z  ∼ 7, a factor of > 70 below our fiducial C II model. When using the standard PCA, this factor is only 0.7 at this redshift. The masking lowers the power amplitude of line contamination down to 2 × 10 −2 Jy 2 sr −1 . This residual level is dominated by faint undetected sources that are not clustered around the detected (and masked) sources. For our C II model, this results in a detection at z  = 5.2 with a power ratio C II /(residual interlopers) = 62 ± 32 for a 22% area survey loss. However, at z  = 7, C II /(residual interlopers) = 2.0 ± 1.4, due to the weak contrast between C II and the residual line contamination. Thanks to the large area covered by SIDES-Uchuu, we show that the power amplitude of line residuals varies by 12–15% for z  = 5.2 − 7, which is less than the field-to-field variance affecting C II power spectra. Conclusions. We present an end-to-end simulation of the extragalactic foreground removal that we ran to detect the C II at high redshift via its angular power spectrum. We show that cosmic infrared background fluctuations are not a limiting foreground for C II LIM. On the contrary, the CO and C I line contamination severely limits our ability to accurately measure the C II angular power spectrum at z  ≳ 7.