  Motivated by a recent experiment in ultracold atoms [ S. Krinner et al.,
Proc. Natl. Acad. Sci. U.S.A 113, 8144 (2016)], we analyze transport of
attractively interacting fermions through a one-dimensional wire near the
superfluid transition. We show that in a ballistic regime where the conductance
is quantized in the absence of interaction, the conductance is renormalized by
superfluid fluctuations in reservoirs. In particular, the particle conductance
is strongly enhanced and the plateau is blurred by emergent bosonic pair
transport. For spin transport, in addition to the contact resistance the wire
itself is resistive, leading to a suppression of the measured spin conductance.
Our results are qualitatively consistent with the experimental observations.
