Using Herschel-SPIRE imaging and the Canada-France Imaging Survey (CFIS) Low Surface Brightness data products from the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS), we present a cross-correlation between the cosmic far-infrared background and cosmic optical background fluctuations. The cross-spectrum is measured for two cases: all galaxies are kept in the images; or all individually-detected galaxies are masked to produce 'background' maps. We report the detection of the cross-correlation signal at ≳ 18 σ (≳ 14 σ for the background map). The part of the optical brightness variations that are correlated with the submm emission translates to an rms brightness of ≃ 32.5 mag arcsec^-2 in the r band, a level normally unreachable for individual sources. A critical issue is determining what fraction of the cross-power spectrum might be caused by emission from Galactic cirrus. For one of the fields, the Galactic contamination is 10 times higher than the extragalactic signal; however, for the other fields, the contamination is around 20 per cent. An additional discriminant is that the cross-power spectrum is of the approximate form P(k)∝1/k, much shallower than that of Galactic cirrus. We interpret the results in a halo-model framework, which shows good agreement with independent measurements for the scalings of star-formation rates in galaxies. The approach presented in this study holds great promise for future surveys such as FYST/CCAT-prime combined with Euclid or the Vera Rubin Observatory (LSST), which will enable a detailed exploration of the evolution of star formation in galaxies.