We report first-principles calculations of shot noise properties of parallel carbon wires in the regime in which the interwire distance is much smaller than the inelastic mean free path. We find that, with increasing interwire distance, the current rapidly approaches a value close to twice the current of each wire, while the Fano factor, for the same distances, is still larger than the Fano factor of a single wire. This enhanced Fano factor is the signature of the correlation between electron waves travelling along the two different wires. In addition, we find that the Fano factor is very sensitive to bonding between the wires, and can vary by orders of magnitudes on changing the interwire spacing by less than 0.5 Å. While these findings confirm that shot noise is a very sensitive tool for probing electron transport properties in nanoscale conductors, they also suggest that considerable experimental control of these structures is required to employ them in electronics.