During his club career Francini played for Torino (1978–87), making his debut in 1980, and during this period he was sent to Serie B side Reggiana on loan for the 1982–83 season, where he could not help the team avoid relegation to Serie C. During his time with the Turin club, he managed to reach three consecutive Coppa Italia finals between 1980–1982, also managing a second-place finish in Serie A in 1985, and he also made his European debut during his time at the club. He later played for Maradona's Napoli side (1987–1994), where he enjoyed another successful period. During this time, he won the Serie A, the Supercoppa Italiana, and the UEFA Cup, also reaching the Coppa Italia final. He moved to Genoa briefly in 1994, and subsequently to Brescia (1994–96), where he retired in 1996, at the age of 32, in Serie B.