Extreme heterogeneity within foreign language instruction in French higher education has led to calls to find common elements to increase coherence. Whereas debates about course content have often emphasized the importance of specificity, the presence of mixed disciplinary groups has complicated the widespread adoption of specialized teaching. We suggest that pragmatics has potential to serve as a common element because it encompasses the study of communicative action both within and outside professional communities and can thus be emphasized in any class, regardless of its degree of specificity. While pragmatic elements are fundamental to contemporary teaching approaches, we argue that these manifestations have not kept up with evolutions in interlanguage pragmatics. In order to show this, we problematize the notion of appropriateness as described in the Common European Framework of References for Languages (CEFR), comparing it with the way that the notion has been treated in contemporary interlanguage pragmatics. Finally, we provide examples of how developments in pragmatics regarding appropriateness have been integrated into both specialized and non-specialized teaching.