Francissca was born into in Malaysia of Ceylonese (Sri Lankan/Scottish) and Chinese family, to Alice Peter and Lucian G. Peter (embraced Islam in 2007 and changed his name to Muhammad Gaberial Peter Abdullah). She is the second of four siblings. Her father — an ex British soldier in the army during Malaya days teaching English grammar to the British soldiers then went on to be one of the first Reuters, Bernama then later joined New Straits Times and then went on to start the New paper, The Straits Echo'. He turned to alcoholism becos he was not happy and was very anti establishment and he eventually abandoned the family in 1978.  Her mother had to raise Francissca and her siblings single-handedly with help from a handful of people and The Canossian Nuns.

Despite being born in Klang, Selangor, Fran spent most of her childhood in Ipoh, Perak. She attended Main Convent Ipoh and then Tarcisian Convent Ipoh. The family moved to Petaling Jaya permanently in 1982 and she was enrolled at a co-ed school in Selayang. Francissca left school after Form Three, took up a typingwriting course, and started working as a salesgirl/rep in a Batik factory and shop for Tourist to help support her family but A year later, with money being tight, Fran took the decision to go into singing. She and her mother scoured through the newspapers together, searching for agents who would help Fran secure a singing job.

After her marriage, Francissca moved overseas - first to the US, then UK, and China (Guangzhou and Hong Kong) - in the 1990s, before relocating back to Malaysia in 2001.