Francis "Bull" McCaffrey (December 26, 1888 – December 26, 1952) was an American football player and coach. McCaffrey was the co-head football coach at Fordham University with Frank Gargan for one season, in 1917, and compiled a record of 7–2. McCaffrey was also the head football coach of Erasmus Hall High School in Brooklyn and DeWitt Clinton High School in the Bronx.