This paper deals with the French periphrasis “s’en aller + Verb in past participle”, which was in use during the 16th and 17th centuries before becoming obsolete. Within the framework of a holistic compositional approach of the construction (Gosselin 1996, 2017), we develop an assumption, according to which the produced meaning marking the impending completion of an action (Gougenheim, [1929] 1971:111) stems from the interaction between the grammaticalization of s’en aller as an auxiliary signifying the abstract movement towards the verb on one hand, and the distensive aspect of the past participle of the verb for the semantic feature of completion on the other hand. We compare the French construction with others in Spanish and Italian.