  We study the wetting of a thin elastic filament floating on a fluid surface
by a droplet of another, immiscible fluid. This quasi-2D experimental system is
the lower-dimensional counterpart of the wetting and wrapping of a droplet by
an elastic sheet. The simplicity of this system allows us to study the
phenomenology of partial wetting and wrapping of the droplet by measuring
angles of contact as a function of the elasticity of the filament, the applied
tension and the curvature of the droplet. We find that a purely geometric
theory gives a good description of the mechanical equilibria in the system. The
estimates of applied tension and tension in the filament obey an elastic
version of the Young-Laplace-Dupr\'e relation. However, curvatures close to the
contact line are not captured by the geometric theory, possibly because of 3D
effects at the contact line. We also find that when a highly-bendable filament
completely wraps the droplet, there is continuity of curvature at the
droplet-filament interface, leading to seamless wrapping as observed in a 3D
droplet.
