The Brexit referendum and the decision of British voters to leave the EU have sparked a comprehensive debate on the future of European integration. A key issue in this debate is the appropriate division of responsibilities between the EU and its Member States. The EU might still lack certain competencies which are crucial for a functioning Union or resilient euro area. At the same time, however, some of the EU’s existing competencies might be better allocated to Member States. This policy brief documents results from a survey on the future of European integration conducted in the national parliaments of both France and Germany, including the French Sénat, the Assemblée Nationale and the German Bundestag, between April and July 2016.