We compute a presentation of the fundamental group of a higher-rank graph
using a coloured graph description of higher-rank graphs developed by the third
author. We compute the fundamental groups of several examples from the
literature. Our results fit naturally into the suite of known geometrical
results about $k$-graphs when we show that the abelianisation of fundamental
group is the homology group. We end with a calculation which gives a
non-standard presentation of the fundamental group of the Klein bottle to the
one normally found in the literature.