I've only just seen your post of last March. I can't tell you anything about your close family, but you can try looking at my previous posts in this forum.
The Frankis family is first clearly recorded in Gloucestershire about 1700, centred in Upton St Leonard but spreading widely throughout that county and also Wiltshire.
In the mid-19th century several members of the family moved to London and their descendents can still be found in the home-counties, especially Essex. I would guess that your ancestors made the shorter move to Birmingham but I have no information about this.
Before 1700 everything is unclear. The name Frankis is probably of Northern English origin and people of that name are recorded in Yorkshire, Northumberland and Cumbria in the middle ages, but whether they have any connection with the family subsequently recorded in Gloucester I don't know.