  Using {\it 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 $\gtrsim 18\,\sigma$
($\gtrsim 14\,\sigma$ for the background map). The part of the optical
brightness variations that are correlated with the submm emission translates to
an rms brightness of $\simeq 32.5\,{\rm mag}\,{\rm arcsec}^{-2}$ 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
$P(k)\propto 1/k$, 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 {\it Euclid} or the Vera Rubin
Observatory (LSST), which will enable a detailed exploration of the evolution
of star formation in galaxies.
