Her son Aidan, who was just 5 months old when she went missing, was at the service with his father Danny Norsworthy - Ms Furlong's boyfriend at the time of her disappearance.
The theme of the service was "found", and mourners who filled the church were told to focus on what they knew of Ms Furlong rather than unanswered questions about her death.
Ms Furlong's mother Judith spoke at the service.
She spoke of a bright and outgoing young woman who was haunted by her troubled life.
Mrs Furlong said she always felt Jane would come through the tough times and sort her life out.
A photo slideshow was played to one of Ms Furlong's favourite songs - Sweet Child O' Mine by 80s rock band Guns N' Roses.
Members of the police team leading the investigation into Ms Furlong's death, named Operation Darlia, also attended the funeral.
Among them was Detective Inspector Mark Benefield, who worked on some of the initial inquiries into Ms Furlong's disappearance.
