Matthew Grevers and Nick Thomas gave the Americans a 1-2 finish in the men's backstroke, but Rebecca Soni had to settle for her second consecutive runner-up finish in the 100-meter breaststroke and nobody had an answer for Frenchman Yannick Agnel in the freestyle.
Michael Phelps, meanwhile, safely reached the finals of the 200-meter butterfly, but he will have a host of challengers on Tuesday in his bid to win the event for the third Olympics in a row.
Franklin, 17, hailed as the next superstar in American swimming, pulled away during the second half of the race to win the women's 100-meter backstroke. She had been a part of the freestyle relay team that won a bronze medal Saturday, but this was the first gold of her career.
She has a chance for more gold medals at these Games and likely will be around to swim in Rio de Janeiro at the 2016 Olympics.
Franklin turned in a U.S. record time of 58.33, which was good enough to down Emily Seebohm of Australia (58.68). Ava Terakawa of Japan collected one of three bronze medals won by her country in the pool Monday.
Grevers and Thoman gave the United States its first gold-silver finish of these Olympics with Grevers setting an Olympic record of 52.16 over 100 meters. Thoman was clocked in 52.92 and Japan's Ryosuke Irie was third in 52.97.
Those performances in the men's and women's backstroke helped ease the pain of missed opportunities by Phelps in the 400-meter individual medley Saturday and the loss to France in the freestyle relay Sunday.
Agnel, the hero of that relay for the French, was at it again Monday when he dominated the 200-meter freestyle. He won in 1:43.14 with Taehwan Park of South Korea and Sun Yang of China finishing in a tie for second almost a full second behind.
American Ryan Lochte, passed by Agnel during the fourth leg of Sunday's relay, wound up fourth in the freestyle.
The United States almost came up with a third gold medal in the pool Monday, but Soni was edged by 15-year-old Ruta Meilutyte of Lithania.
Soni, a notoriously slow starter, came within .08 of a second of catching the youngster after finishing second to Australian Leisel Jones in the same race at Beijing. Satomi Suzuki of Japan was third.
Phelps won his semifinal heat in qualifying for Tuesday's 200-meter butterfly, but three swimmers in the other heat had a faster time than he did. He will have to contend with Japan's Takeshi Matsuda, South African Chad le Clos and China's Chen Yin to win his first gold medal of the London Olympics.
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