Article II, Section 2 of the Constitution declares that the president "shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur." But it doesn't say anything about the power to break treaties.
The XYZ affair led to a period of anti-French sentiment in the United States, which was problematic as the French has been the key ally during the American revolution some 20 years before and was one of the primary reasons the United States was able to defeat Great Britain.
However, over those 20 years, France had undergone a revolution of their own and the United States decided to remain neutral in France's war against Great Britain.
(As i have heard from my teacher) there are only 8 wonders in the world of ancient civiliazations..! :)