Love Story finally tackled John F. Kennedy Jr. and Carolyn Bessette's infamous public park fight - but there were many other real-life moments in the show that relied on accuracy. "There were two moments that ratcheted up the fame of Carolyn Bessette. The first was this fight in the park since it was one of the first viral videos. Suddenly this very public fight with a Kennedy was splashed all over the news," executive producer Brad Simpson exclusively told Us Weekly during a joint interview with Nina Jacobson. "John got a real lecture internally from the family about it. They're not supposed to show these sorts of things in public." Simpson called it a "real lesson" for Bessette. "It matched up with some of her fears about losing her privacy," he noted. Then the second [moment] was the wedding photograph of their private, secret wedding. That one photograph of her in a very simple dress in front of a very simple church changed weddings and changed wedding dresses for decades. It also made her incredibly famous." How the 'Love Story' Cast Compares to Real Members of the Kennedy Family The creative time wanted to get all the key moments right - starting with the fight in Battery Park. "We knew there was tension because she had not accepted his proposal yet. We knew that he was taking the ring off of her. We knew where they were during the fight and that sometimes it got really intense that she tackles him at one point," Simpson explained. "At another point, they're looking miserable on a bench. At another point, they're crying and making up. We had enough information about the tension in their marriage for [writer] Kim Rosenstock to really construct what we feel was the fight." FX He continued: "We thought what are the fights you have for most couples and what people relate to? What I think [with] capturing people on the show is that a lot of the things that they face - meeting the other person's family and not being totally accepted by the family and not knowing that they want their life to change - these are things that other people have felt, just not on that intense of a level." Love Story: John F. Kennedy Jr. & Carolyn Bessette premiered earlier this month and explores the "undeniable chemistry, whirlwind courtship and high-profile marriage of one of the most iconic couples of the 20th century," according to the synopsis. The FX series is the first installment in Ryan Murphy's Love Story anthology and is inspired by Elizabeth Beller's book Once Upon a Time: The Captivating Life of Carolyn Bessette Kennedy. Sarah Pidgeon plays Bessette, while Paul Anthony Kelly portrays JFK Jr. JFK Jr. and Carolyn Bessette-Kennedy's Relationship Timeline After meeting in 1992, Bessette and JFK Jr. were on and off for years before getting married. Their relationship was thrust into the spotlight with highs and lows making headlines. They both died in a plane crash in 1999. Eric Liebowitz/FX "We had Elizabeth Beller's book for reference, but we did face challenges [capturing certain moments]. They died so young, but we had enough information from people around them to know what the problems were in their marriage, what the tensions were, what the highs were, what the lows were," Simpson told Us. "People don't have an idea of what her voice was like because we only have a tiny clip of her voice, but they have a very distinct idea of what her image was like. So we had to get the walk down and the look and the allure. But Sarah could really interpret and go with it. John, we have a lot of recordings of him, and we have a lot more on him." Looking ahead, Simpson and Jacobson are hopeful that viewers see the care that went into telling Bessette and JFK Jr.'s story. "We loved these characters. We fell in love with them, and it is essential that the audience loved them too. So we knew that we came to it from a very honest and earnest place - and that the show was never meant to dunk on either one of them in any way," Jacobson explained. "We knew from the beginning that we were coming in with love and respect for these characters and that we wanted the audience to share that with us." New episodes of Love Story air Thursdays at 9 p.m. ET on FX and stream on Hulu the next day.