Motivated by a recent experiment in ultracold atoms [S. Krinner et al., Proc. Natl. Acad. Sci. U.S.A. 113, 8144 (2016)PNASA60027-842410.1073/pnas.1601812113], 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 conductance 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.
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