When you originally asked this question, it was in the James Madison section but it only read “did he repeal the Embargo Act?” Therefore, I assume that “he” refers to James Madison. If that is the case, the answer is “no.” James Madison was not in a position where he could repeal the Embargo Act. Instead, it was Congress that passed the law repealing this act and it was President Thomas Jefferson who signed it. This was done in the last days of Jefferson’s presidency, in March of 1809. (In those days, presidents’ terms began in March, not in January as they do now.)
During this time, James Madison was the Minister to Great Britain. The term “minister” was used at that time to refer to a person that we would now call an ambassador. In this capacity, Madison was very much involved in trying to keep relations between the United States and Great Britain friendly. However, he was not able to succeed in this. Because relations between the two countries deteriorated, Jefferson felt it necessary to impose the Embargo Act. Public uproar, along with economic problems caused by the embargo, influenced him to go along with repealing the act. So, the act was repealed, but it was not Madison who repealed it.