Falkholt was born on 15 May 1988 in Sydney to a Swedish father and an Italian mother, Lars and Vivian. She attended Gilroy College in Castle Hill, and was awarded the Higher School Certificate in 2006. She obtained a Bachelor of Arts in Media and Communication at the University of NSW, where she starred in several theatrical productions including the musical Cabaret. After graduation, she worked production jobs at Channel Seven and Carnival Films, building a portfolio by acting in television commercials.
In 2012, Falkholt was accepted into the National Institute of Dramatic Art. While studying there, she had minor television roles in Tricky Business and Underbelly: Badness. A year after graduating from NIDA, she took on the recurring role of Hope Morrison in the long-running series Home and Away. This led to her being cast in her first major role as the title character in the upcoming film Harmony. She also filmed a role in Nine Network's drama Bite Club.
On 26 December 2017, Falkholt was involved in a car crash which killed both her parents instantly. As the vehicle burst into flames, both Jessica and her sister Annabelle, aged 21, were pulled out of the vehicle alive, but Annabelle died on 29 December in Liverpool Hospital. The 50-year-old driver of the other vehicle, who was also killed, was reportedly a serial traffic offender. His car failed to negotiate a curve on the Princes Highway, near Sussex Inlet, and travelled into the path of the Falkholts' car. The Falkholts were returning to Ryde after attending Christmas celebrations. Officials confirmed the driver was returning home to Ulladulla, after visiting a methadone clinic in Nowra. Police are investigating whether the drug was a factor in the crash, among other contributing factors.
Following the crash, Falkholt was taken to Sydney's St George Hospital, where she underwent surgery that included the removal of a kidney and part of her skull. On 12 January 2018, a spokesperson for St George Hospital confirmed that her life support had been turned off. She died in hospital on 17 January 2018 at age 29.
