  Fomalhaut is a triple system, with all components widely separated (~1E5 au).
Such widely separated binaries are thought to form during cluster dissolution,
but that process is unlikely to form such a triple system. We explore an
alternative scenario, where A and C form as a tighter binary from a single
molecular cloud core (with semimajor axis ~1E4 au), and B is captured during
cluster dispersal. We use N-body simulations augmented with the Galactic tidal
forces to show that such a system naturally evolves into a Fomalhaut-like
system in about half of cases, on a timescale compatible with the age of
Fomalhaut. From initial non-interacting orbits, Galactic tides drive cycles in
B's eccentricity that lead to a close encounter with C. After several close
encounters, typically lasting tens of millions of years, one of the stars is
ejected. The Fomalhaut-like case with both components at large separations is
almost invariably a precursor to the ejection of one component, most commonly
Fomalhaut C. By including circumstellar debris in a subset of the simulations,
we also show that such an evolution usually does not disrupt the coherently
eccentric debris disk around Fomalhaut A, and in some cases can even produce
such a disk. We also find that the final eccentricity of the disk around A and
the disk around C are correlated, which may indicate that the dynamics of the
three stars stirred C's disk, explaining its unusual brightness.
