Wilson's program for the peace of Europe failed because the US senate failed to accept The League of Nations.
The League of Nations, a precursor to the United Nations, was the first international and intergovernmental organization and its main aim was to prevent another major war (like WWI) and maintain international peace. It was created at the end of World War I. In the simplest terms, the idea behind the League was that if one of its members were attacked by any country, it would be considered a declaration of war against all the other members as well. In such a scenario, the league would direct its members to take appropriate collective action, whether militarily or economically or by some other means. It also was thought to provide a platform for solving disputes through negotiations and arbitration instead of war.
However, major powers kept out of it due to their own personal agenda, because they did not like the idea of being told by the League what to do, but also that their financial interests may have been compromised in some situations. President Woodrow Wilson was the champion of the League, however, he could not get the US Congress to accept it, especially since Republicans were against it.
This was one of the main reasons for the failure of the League and hence Wilson could not ensure peace in Europe post WWI.