Mieuli was a minority shareholder of both the San Francisco Giants and the San Francisco 49ers prior to the Warriors arrival in the Bay Area in 1962. In a joint venture with Diners Club corporation, Mieuli helped put together a group of local investors to lure the Warriors out of Philadelphia.
Mieuli also produced the 49ers radio broadcasts on KSFO beginning in the 1950s, and produced the first televised 49ers game in 1954. He subsequently produced Giants radio broadcasts, hosted by Russ Hodges and Lon Simmons upon the team's move from New York by owner Horace Stoneham in 1958.
Mieuli was influential in the hiring of sportscaster Bill King, who initially served as the third man in the Giants broadcast booth in 1958, behind Hodges and Simmons. Upon Mieuli's purchase of the Warriors in 1962, King left Giants radio to become play-by-play voice of the newly minted "San Francisco Warriors". Coincidentally, at the time of Mieuli's purchase of the team, he was still producing the radio broadcasts of both the Giants, 49ers, and, the Warriors for KSFO.
In 1956, Mieuli purchased five reel-to-reel audiotape duplicators from Ampex for use in distributing sports and music programming to radio stations. The venture led him to create Hi*Speed Duplicating Company, the first business of its kind in Northern California. In 1960, Mieuli produced national radio coverage of the VIII Winter Olympic Games at Squaw Valley. His firm, Franklin Mieuli & Associates, also produced broadcasts for the Oakland Raiders and Oakland Athletics at various times.
On January 8, 1958, Mieuli was granted a construction permit for a new FM radio station in San Francisco, which went on the air on Thursday, December 10, 1959, as KPUP (106.9 FM; the station is currently the latest version of KFRC). Reflecting Mieuli's love for the style of music, KPUP programmed a Jazz music format, drawing from the rich variety of artists and recordings that were popular at the time, as well as Mieuli's friendship with Saul Zaentz of Fantasy Records. (The San Francisco Giants' 1962 season highlights, narrated by Russ Hodges and Lon Simmons and produced by Mieuli, were released on a long-playing record by Fantasy, catalog number GB-1962.)
KPUP's call letters were changed to the jazzier-sounding KHIP in July 1960. In order to help finance his purchase of the Warriors, Mieuli sold KHIP to Leon Crosby in June 1962 for $146,000; Crosby renamed the station KMPX.
In 2007, Mieuli was inducted into the Bay Area Radio Hall of Fame as a member of the second class to be honored. He was the recipient of five Super Bowl rings as a part-owner of the 49ers, as well as one NBA Championship trophy as the owner of the Warriors.