  We study a model of Tensorial Group Field Theory (TGFT) on $\mathbb{R}^3$
from the point of view of the Functional Renormalisation Group. This is the
first attempt to apply a renormalisation procedure to a TGFT model defined over
a non-compact group manifold. IR divergences (with respect to the metric on
$\mathbb{R}$) coming from the non-compactness of the group are regularised via
compactification, and a thermodynamic limit is then taken. We identify then IR
and UV fixed points of the RG flow and find strong hints of a phase transition
of the TGFT system from a symmetric to a broken or condensate phase in the IR.
