This study starts by testing the assumption that with access to the full range of properties of the language faculty, L2 learners are ultimately successful in assigning target-like meanings to overt forms. A further assumption that can be (implicitly) drawn from this assumption is that L2 pragmatic processes are native-like at Logical Form (in Relevance-theoretic terms, Sperber and Wilson 1986/95). The study focuses on the L2 acquisition of the distributional and interpretational properties of the English present simple (e.g. I cycle to work) and the English present progressive (e.g. I’m cycling to work). Data from advanced L1 French speakers, under varying task conditions, are presented to evaluate these assumptions. In light of any evidence indicating persistent form-meaning mismatches, the results are used to (i) discuss a permanent syntactic deficit as the possible source of difficulty in acquiring target-like form-meaning relationships and (ii) consider the potential implications for pragmatic processes resulting from this deficit.