Global Fragility Act of 2019 This bill directs the President to devise and implement a plan to combat global fragility. The bill also establishes funds to support such endeavors. The President shall report to Congress and implement a 10-year Global Fragility Strategy to (1) help stabilize conflict-affected areas, (2) address global fragility, and (3) increase U.S. capacity to be a leader in international efforts to prevent extremism and violent conflict. The strategy shall (1) focus on the long-term causes of fragility and violence; (2) include specific objectives and approaches to reduce such causes; and (3) contain a selection of priority countries and regions based on various factors, including U.S. national security interest and clearly defined indicators of the levels of violence or fragility in a country or region. The President shall report to Congress and implement action plans for the priority countries and regions. The bill establishes the Prevention and Stabilization Fund to replace the Relief and Recovery Fund. The new fund shall support stabilization of conflict-affected areas and assist areas liberated from or at risk from various terrorist organizations such as the Islamic State of Iraq and Syria. The bill also establishes the Complex Crises Fund to prevent or respond to emerging and unforeseen events overseas.