You’re right: I was thinking his initial arrival in the Senate was by gubernatorial appointment, but it was by special election.
When Gore gave up his Senate seat, the Democrat governor of Tennessee, Ned Ray McWherter, appointed Harlan Mathews to the seat. In November 1994 there was a special election to choose who would serve out the remaining two years, which Fred won (Mathews wasn’t a candidate), and he was sworn in a month later in Dec. 1994...then beat Jim Cooper in a regular election in 1996.