Find Ancestors

Hi. New to all this. Have just found through this site, that I have family on my father's side in Australia. It got me thinking, that I know very little about my mother's side of the family. I don't know where to start. My mother was Marie Jean Winter (nee Groom) born December 1st 1919. I think in Bristol?? certainly grew up there, and Married my father Walter H Winter in 1939. I think my Grandmother on my mother's side died when my mother was quite young. My mother also told me once that she believed her mother was French. I would dearly love to find out about mum's family. My Grandfather I think was called Alfred Groom. i think mum had a sister/half sister called Lilian?? Bit sketchy. Please can someone give me some pointers as to how I go about finding any info. Thanks so much.