Angel anchored France's 400-meter freestyle relay team to a victory over the Americans, reversing the outcome in Beijing four years ago.
On that occasion the United States won the relay by .08 of a second, giving Michael Phelps one of the record eight gold medals he brought home from China.
This time the French came from behind to win by almost a half second despite an excellent second leg swum by Phelps that appeared to have started the Americans on their way to victory.
The relay triumph was one of two by the French in Olympic swimming Sunday, the other one turned in by Camille Muffat in the women's 400-meter freestyle. She also fought off an American -- Allison Schmidt.
The United States won four medals in the four swimming events contested Sunday, but only one was gold. That came from favorite Dana Vollmer in the 100-meter butterfly, where she established a world record of 55.98.
Cameron van der Burgh of South Africa won the 100-meter breaststroke, giving his country its first medal of the Olympics.
Because Phelps was able to finish only fourth in the 400-meter individual medley on Saturday, his level of fitness was being questioned heading into Sunday's relay.
Phelps answered those questions, however, turning an excellent second leg and putting the Americans well in front.
Their lead began to fade during the third leg, however, and Angel made up the rest against Lochte -- who won the individual medley on Saturday.
France was timed in 3:09.93 while the United States finished in 3:10.38. Russian finished third, shutting out an Australian team that was a medal favorite.
The silver won by Phelps was the 17th medal of his Olympic career, leaving him one away from equaling the all-time record. He is expected to swim in five more events in London.
Vollmer added her Olympic gold to the world championship she won last year. She beat China's Lu Ying by almost a second while Australia's Alicia Coutts was third.
Muffat won her gold medal by .32 of a second over Schmitt. Rebecca Adlington of Britain took the bronze in the 400-meter freestyle.