  Finite modular family symmetry can emerge from top-down approaches based on
heterotic string theory or Type IIB string theory. We show that, in addition to
such approaches, it can also emerge from local F-Theory bottom-up
constructions. As a first example of the new approach, we have analysed in
detail a concrete F-Theory Fluxed $SU(5)$ Grand Unified Theory (GUT) with
modular $S_4$ family symmetry. The model fits the fermion mass and mixing data
very well and serves as a demonstration of the bottom-up approach to modular
family symmetry in F-Theory fluxed GUTs.
