This action research-based doctoral thesis concerns course content and language-learning objectives in the sector of L2 teaching in France for students in higher education who are not specializing in that language, a sector known as Languages for Specialists of Other Disciplines (LANSOD). Discussions about LANSOD course content often refer to the appropriate degree of specificity for these classes in line with a Languages for Specific Purposes (LSP) perspective. However, in this work, we will question the utility of a specificity continuum ranging from “general” to specific” language teaching, particularly due to the ambiguity of the concept of “general language.” Instead, we will suggest that the development of flexible pragmatic skills is a more pertinent objective than “general language skills” for groups of students with undetermined or varied language needs. In order to explore this argument, we selected a classroom of second-year undergraduate students in the field of Culture and Media at the University of Lille because of the students’ varied needs and implemented a series of pedagogical initiatives based on genre-based text analysis and description to develop the students’ flexible pragmatic competence in English. Results show that our approach elicited a variety of interesting pragmatic insights from students even though the notions of genre and context proved more difficult to deal with than we had foreseen. Since the field of pragmatics is producing increasingly sophisticated approaches to the study of communication and context, we conclude that this field offers promising insights for LANSOD course content specification, particularly with regards to the lens that it offers on specificity.