I am pretty sure it is spelt Froomes but it could possibly be Frooms.
The closest connection to myself with this name is Isabel Froomes born 1871. Was my great great grandmother. Would have lived in Victoria, Australia. She maried a John Rigby. Her father was a Henry Froomes, who married a Sarah Belcher, as far as I have been able to work out. I am not sure at what time he would have been born, but it would probably have been in the early to mid 1800s.
Does anyone at all have any more info on these names?