"I can find no case of a former president subsequently becoming a senator."

A couple of posts prior to yours, JotSC, the link provided by Ebbie tells us that Andrew Johnson served as Senator from Tennessee after his Presidency.

Johnson is easily forgotten, I suppose, not having been elected. He was Lincoln's second VP and succeeded to the Presidency subsequent to the assassination. His former claim to fame, as the only US President ever to be impeached, was stolen from him by one William Jefferson "Bubba" Clinton.