  It has recently been shown that interference effects in disordered systems
give rise to two non-trivial structures: the coherent backscattering (CBS)
peak, a well-known signature of interference effects in the presence of
disorder, and the coherent forward scattering (CFS) peak, which emerges when
Anderson localization sets in. We study here the CFS effect in the presence of
quantum multifractality, a fundamental property of several systems, such as the
Anderson model at the metal-insulator transition. We focus on Floquet systems,
and find that the CFS peak shape and its peak height dynamics are generically
controlled by the multifractal dimensions $D_1$ and $D_2$, and by the spectral
form factor. We check our results using a 1D Floquet system whose states have
multifractal properties controlled by a single parameter. Our predictions are
fully confirmed by numerical simulations and analytic perturbation expansions
on this model. Our results, which we believe to be generic, provide an original
and direct way to detect and characterize multifractality in experimental
systems.
