We present a construction of the fractional $Φ^4$ Euclidean quantum field theory on $\mathbb{R}^3$ in the full subcritical regime via parabolic stochastic quantisation. Our approach is based on the use of a truncated flow equation for the effective description of the model at sufficiently small scales and on coercive estimates for the non-linear stochastic partial differential equation describing the interacting field. The measure is invariant under translations, reflection positive and has quartic exponential tails.