The opposition between sovereignist/nationalist and cosmopolitan discourses is extremely ancient and keeps on heightening tensions in contemporary Europe and beyond. While a wide array of academic works concentrates nowadays on how nationalist and right-wing populist discourses are constructed and how they gain ground all over the world, a discursive study of cosmopolitanism is still lacking (Cicchelli 2016, 46). Willing to fill that gap, this paper proposes a focus on the discursive features of a cosmopolitan-inspired discourse deployed in British and French media in 2016-2019. Nevertheless, the study is not dealing with a cosmopolitan discourse separated from any circumstances of its emergence. By contrast, I am particularly interested in the modalities of its construction while facing an opposing discourse: for instance, a pro-Brexit and anti-cosmopolitan speech by Theresa May. It will be argued that this "conceptual conflict" targeting the notion of "citizen of the word" as discursively (un)acceptable is particularly suitable for a study of what it means nowadays to deploy a cosmopolitan discourse. The analysis of discursive features of such a conflict (including definition process, construction of addressees, motifs, metadiscourse and shared frameworks) is conducted in order to understand how these two discourses seek for legitimacy while their relationship is characterized by a significant power imbalance. The papers show that even though cosmopolitan discourses strive to de-legitimate sovereignist ones and expand the boundaries of "sayable" to the concept of "citizen of the world", they also exercise a form of self-censorship and remain dependent on these very boundaries they are trying to redefine.