Plasmonic circular dichroism (CD) of chiral molecules in the near field of plasmonic nanoparticles (NPs) may be used to enhance molecular CD signatures or to induce a CD signal at the plasmon resonance. A recent few-states theory explored these effects for model systems and showed an orientation dependence of the sign of the induced CD signal for spherical NPs. Here, we use the discrete interaction model/quantum mechanical (DIM/QM) method to simulate the CD and plasmonic CD of the 310- and α-helix conformations of a short alanine peptide. We find that the interactions between the molecule and the plasmon lead to significant changes in the CD spectra. In the plasmon region, we find that the sign of the CD depends strongly on the orientation of the molecule as well as specific interactions with the NP through image dipole effects. A small enhancement of the CD is found in the molecular region of the spectrum, however, the molecular signatures may be significantly altered through interactions with the NP. We also show that the image dipole effect can result in induced plasmonic CD even for achiral molecules. Overall, we find that the specific interactions with the NP can lead to large changes to the CD spectrum that complicates the interpretation of the results.