This paper explores the challenges of the Eurozone's monetary union, focusing on the coordination issues between its unified monetary policy and diverse fiscal policies, which significantly influence public debt and price stability. It further investigates the extent to which a fiscal union issuing Eurobonds could address this coordination issue. The key finding is that the policy-mix consistent with a unique equilibrium critically depends on the structure of financial markets and on the level of financial frictions. While Eurobonds can effectively resolve the coordination issue in complete markets, achieving a unique equilibrium in incomplete markets proves to be more complex.