The batsman can only be Run Out in this situation if it is attempting to score by running between the creases. If no such attempt is made, the batsman is Stumped instead (Law 39.1, Out Stumped and Law 38.2.b, Batsman not Run Out).
As a delivery is a free hit, the batsman cannot be out Stumped (Law 28.17, Out from a No ball, which is further applied to the free hit itself). Whether the batsman was or was not attempting to run between the creases cannot be determined by anybody who was not present and does not have access to conclusive video or audio evidence.
In the case that it is not clear even to witnesses or by examination of evidence (and in particular, it is not clear to the umpires of the match in question) benefit of the doubt is presumed for the batsman (Law 27.6, Consultation by umpires), and therefore the decision should be not out.