McCain, 73, died of respiratory problems, his son, Franklin Jr., told the New York Times.
A lifelong North Carolina resident, McCain spent much of his adult life in Charlotte, where he worked for Celanese Corp., the (Charlotte) Observer reported. He spent his last years in Greensboro, where he died.
While McCain had a successful life, raising three sons with his wife, Bettye, who had also been in the civil rights movement, and chairing the board of his alma mater, North Carolina A.&.T, he remained best-known for his actions as a 19-year-old as one of the "Greensboro Four." He and three friends made some small purchases in the F.W. Woolworth's store in downtown Greensboro and then sat down at the lunch counter.
Several employees, at least one of them black, told them to leave. An elderly white woman put her hands on two of the young men's shoulders as she departed and they expected a tirade.
"I was convinced we were going to get an earful," McCain said decades later. "But then she said, 'Boys, I am so proud of you. I only wish you'd done this 10 years ago.' "
The sit-in grew and Woolworth's, within days, integrated its lunch counter. It inspired similar actions elsewhere in the South and the founding of the Student Non-Violent Coordinating Committee.
"To the world, he was a civil rights pioneer who, along with his three classmates, dared to make a difference by starting the sit-in movement," Franklin Jr. told the Observer on Friday. "To us, he was Daddy -- a man who deeply loved his family and cherished his friends. We will forever treasure the wonderful memories that we have and be thankful for all that he did for us and for his fellow man."
The former Woolworth's is now the International Civil Rights Center & Museum and part of the lunch counter is in the Smithsonian Museum of American History.
"Before the march on Washington, Montgomery and Birmingham, there was the walk to Woolworth's," a poster in the Greensboro museum says.