How Princess Diana’s Death 'Rattled' Carolyn Bessette Kennedy – and Left Her 'Terrified' of the Paparazzi

The moment she married JFK Jr. in 1996, Carolyn Bessette became one of the most famous women in the world.

The sudden spotlight wasn’t always easy for the new bride. Whereas John’s mother, Jacqueline Kennedy Onassis, had time to grow accustomed to her fame, first as a senator’s wife and then as First Lady, Carolyn’s transition was far more abrupt. “It was much slower for Jackie,” says friend John Perry Barlow, who knew both Jackie and Carolyn. “And it was a different kind of celebrity, too. Because people tended to be favorably inclined toward Jackie.”

In this week’s PEOPLE, some of Carolyn’s closest friends reveal new details about the woman the public never got a chance to know, including how she was unsettled by Princess Diana’s death in a 1997 car crash after being chased by paparazzi.

Afterward, she feared the paparazzi would become more aggressive toward her and John. “At the time, John and Diana were the two most famous people in the world,” says RoseMarie Terenzio, who worked as John’s executive assistant at George magazine and became a close friend. “Carolyn was horrified by Diana’s death. She worried about her children and how they’d grow up without their mom. But she was also rattled by the fact that it could happen to John—that it could happen to her. She feared, ‘Now they’re going to focus on us even more because they don’t have her.’ “

While John was also saddened by Diana’s death, he kept it more to himself. “The more things were amplified, the less he would show it,” recalls Terenzio, whose 2012 memoir, Fairy Tale Interrupted, chronicles her close friendship with John and Carolyn. “He felt bad for her and her family, but to him it was a no-win situation. The press was not going to go away.”

Although John tried to give Carolyn advice on how to handle the spotlight, she couldn’t shake her fears.

In her recent memoir Jackie’s Girl, Kathy McKeon, who worked for the former First Lady as her assistant and part-time nanny after President John F. Kennedy’s death, recounts a weekend she and her husband, Seamus McKeon, spent in Hyannis Port.

It was also the day of Princess Diana’s funeral on September 6, 1997. “We talked about it that night,” recalls Kathy. “John said, ‘Tell Carolyn how my mom handled photographers.’ I said, ‘She was nice to them—she smiled and gave them one good picture.’ He said, ‘Carolyn, did you get that? You’re treating them all wrong.’ She said, ‘I hate those bastards.’ “

“She told us about them cornering her and running and chasing her into a building and they were right on top of her,” adds her husband Seamus. “She said, ‘I’m terrified of them.”

“She couldn’t take that,” says Kathy. “She wasn’t brought up with it. John was. Carolyn wasn’t. She wanted peace and quiet and for nobody to bother her.”

For more on Carolyn Bessette Kennedy, pick up a copy of this week’s PEOPLE.