Harris attended Penn State University and was the blocking back for future Pro Bowl running back Lydell Mitchell. In the 1972 draft he was chosen by the Pittsburgh Steelers in the first round, the 13th selection overall. He played his first 12 years in the NFL with the Steelers; his 13th and final year (1984) was spent with the Seattle Seahawks. 

In his first season with the Steelers (1972), Harris was named the league's rookie of the year by both The Sporting News and United Press International. In that season he gained 1,055 yards on 188 carries, with a 5.6 yards per carry average. He also rushed for 10 touchdowns and caught 3 touchdown passes. He was extremely popular with Pittsburgh's large Italian-American population: his fans dubbing themselves "Franco's Italian Army."

Harris was the key to one of the most famous plays in football, the Immaculate Reception, so dubbed by Pittsburgh sportscaster Myron Cope. In a 1972 playoff game, the Oakland Raiders were leading the Steelers by 7-6 with 22 seconds to play when a Terry Bradshaw pass was deflected -- off of Raiders defensive back Jack Tatum, the officials ruled. Harris snatched the ball just before it hit the ground and ran it in to win the game.

Harris was chosen for 9 consecutive Pro Bowls from 1972 through 1980, and was All-Pro in 1977. He broke Jim Brown's record by rushing for more than 1,000 yards in 8 seasons. The tandem running package of Harris and Vietnam veteran Rocky Bleier combined with a strong defense to win four Super Bowls in the 1974, 1975, 1978, and 1979 seasons. In 1975 he was the Most Valuable Player of Super Bowl IX; in that game he rushed for 158 yards on 34 carries for a 16-6 win over the Minnesota Vikings.

In his 13 professional seasons, Harris gained 12,120 yards on 2,949 carries, a 4.1 yards per carry average, and scored 91 rushing touchdowns. He caught 307 passes for 2,287 yards, a 7.4 average, and 9 touchdowns.

Harris has spent much of his post football career owning various food businesses.