Climate change and migration are two prominent subjects of intense concern occupying public and political debate today. Since the mid-1980s, a growing academic and policy literature has sought to characterise the relationship between them. From the outset, this literature grappled with major conceptual, practical, and political questions. What is the causal relationship linking climate change to migration? Where is climate migration occurring? What responses does it call for, and what principles should guide interventions? These questions remain largely unresolved today. A clear definition of climate migration remains elusive, as do projects to address rather than simply study the phenomenon. In this thesis, I argue that understanding the unresolved ambiguities and uncertainties that characterise climate migration debates requires paying close attention to how knowledge about climate migration is produced and circulated. To this end, I develop an 'epistemic mobilities' approach to climate migration, drawing on prior work on 'travelling ideas' by historians and sociologists of knowledge (and on cognate concepts in related disciplines). Focusing on the French context, I ask who participates in climate migration debates, how they define and represent it, and the reasoning behind the responses they propose. Methodologically, I use interviews with development practitioners (at the Agence Française de Développement and in non-governmental organisations), knowledge producers (academics and journalists) and politicians. I analyse the documents produced and cited by these stakeholders and conduct a corpus-driven analysis of news media coverage about climate migration. In the analysis, I triangulate these three sources of information and bring them in conversation with the academic literature. I describe an unstable and fragmented stakeholder network marked by persistent tensions. On the one hand, climate migration is seen as a self-evidently real phenomenon requiring a response. On the other, and in a political context marked by widespread hostility towards migrants, stakeholders continue to disagree on the usefulness of causal claims linking climate change to migration. Further, I show that dominant practices used to represent climate migration only serve to reinforce these tensions. French stakeholders never successfully locate climate migration in a "here and now" amenable to intervention. Finally, I also highlight simultaneous and contradictory attempts to politicise and depoliticise responses to climate migration, as evidenced by debates about responsibility and justice. Having underscored the contingent nature of climate migration debates, I conclude the thesis by comparing my French case study with other countries, suggesting that many of the issues faced by French stakeholders are likely to apply in other contexts.