I can find no case of a former president subsequently becoming a senator. John C. Calhoun resigned the Vice-Presidency in 1832 to run for and become Senator from S. Carolina. The reason for this...he had favored States Rights issues in opposition to the President (Jackson).
As you may remember from US History, South Carolina was always a hotbed for states rights, and it was there that the Civil War began a quarter of a century later.