The XYZ Affair and the Quasi-War with France, 1798–1800. The XYZ Affair was a diplomatic incident between French and United States diplomats that resulted in a limited, undeclared war known as the Quasi-War. U.S. and French negotiators restored peace with the Convention of 1800, also known as the Treaty of Mortefontaine. Elbridge Gerry. In the late 1700s, the final French Revolutionary government, the Directory, was experiencing problems financing its European wars. Many leaders were also angry that the United States had concluded the Jay Treaty with Great Britain in 1794.