In this paper, we propose a pragmatic solution to the French surcomposé (double composed) past tense (SPT) puzzle, after we first draw a global contrastive picture of double composed pasts. The puzzle raised by French SPT is that it presents a particularly strong variation between standard French, reflected in classical grammars, which clearly rejects SPT independant clauses (without a temporal adverb), and Southern areas, including Switzerland, where such independant clauses are felt perfectly natural. The paper suggests that in all cases SPT calls pragmatically for relevance at a particular point on the timeline; Standard French allows only SPT to call for relevance at the(past) reference point (R in Reichenbach 1947), whereas Southern varieties of French also allow SPT utterances to bear relevance in the very present of speech in the form of a potentiality, a case which happens only with independant clauses. After reviewing the solutions on offer on the semantics and pragmatics of the French SPT, we develop a unified semantic and pragmatic account for which the diatopic variation does not counter the assumption of a specific semantic common basis for all types of SPT-utterances.