Charge transfer at the interface of conjugated polymer and nanoscale inorganic acceptors is pivotal in determining the efficiency of excitonic solar cells. Despite intense efforts, carbon nanotube/polymer solar cells have resulted in disappointing efficiencies (<2%) due in large part to poor charge transfer at the interface. While the interfacial energy level alignment is clearly important, the self-assembly and the interface structure also play a major role in facilitating this charge transfer. To understand and control this effect to our advantage, we study the interface of commonly used conductive polymer poly-3-hexylthiophene (P3HT) and single-walled carbon nanotubes (SWNTs) with a combination of molecular dynamics simulations, absorption spectra experiments, and an analysis of charge transfer effects. Classical molecular dynamics simulations show that the P3HT wraps around the SWNTs in a number of different conformations, including helices, bundles, and more elongated conformations that maximize planar π-π stacking, in agreement with recent experimental observations. Snapshots from the MD simulations reveal that the carbon nanotubes play an important templating role of increasing the π-conjugation in the system, an effect deriving from the π-π stacking interaction at the interface and the 1-dimensional (1D) nature of the SWNTs, and independent of the SWNT chirality. We show how this increase in the system conjugation could largely improve the charge transfer in P3HT-SWNT type II heterojunctions and support our results with absorption spectra measurements of mixtures of carbon nanotubes and P3HT. These findings open possibilities for improved preparation of polymeric solar cells based on carbon nanotubes and on 1D nanomaterials in general.