We present high-resolution (R ~ 15 000) VLT/UVES optical spectra of two planetary nebulae (PNe; Tc 1 and M 1-20) where C60 (and C70) fullerenes have already been found. These spectra are of high quality (S/N > 300) for PN Tc 1, which permits us to search for the expected electronic transitions of neutral C60 and diffuse interstellar bands (DIBs). Surprisingly, we report the non-detection of the most intense optical bands of C60 in Tc 1, although this could be explained by the low C60 column density estimated from the C60 infrared bands if the C60 emission peaks far away from the central star. The strongest and most common DIBs in both fullerene PNe are normal for their reddening. Interestingly, the very broad 4428 Å DIB and the weaker 6309 Å DIB are found to be unusually intense in Tc 1. We also report the detection of a new broad (FWHM ~ 5 Å) unidentified band at ~6525 Å. We propose that the 4428 Å DIB (probably also the 6309 Å DIB and the new 6525 Å band) may be related to the presence of larger fullerenes (e.g., C80, C240, C320, and C540) and buckyonions (multishell fullerenes such as C60@C240 and C60@C240@C540) in the circumstellar envelope of Tc 1. Appendix A is available in electronic form at http://www.aanda.org