My Great Grandfathers uncle Johny Breen is recorded on the 1911 census for Ireland, as living at Owenbreedin, Brookeborough Co. Fermanagh. In fact this townland/farm is opposite my home - I can see the house from were I am sitting! Johny Breen was married in 1865 to a Mary Mc Donagh and as far as I know had 7 children Ellen (1867) Andrew (1869) John (1871) Hughie (1873) Mary Anne (1877) Michael (1881) and Patrick (1879. I know that Hughie's wife was called Mary Jane and they resided and died here on the farm where I live.
I have no idea how your James is related to my Great grandfather Patrick who was born in Brookeborough in 1869. As far as I know my great grandfather had a brother James born 1867. Their parents are Hugh Breen who was marrried to Mary Foy.
If you look at the 1901 census for Ireland you will see that Anne Breen is 31 years old and she is widowed with two sons James age 9 and Edward age 7.
The Hugh and Ellen Breen are in a different household and are aged 6oyrs. Don't think they could be parents to your James! They have a 20year old daughter, Catherine and a 5 year old grandson Joseph living with them.
Can't find Anne and her two sons James and Edward on the 1911 census. Maybe she is remarried but should still be able to find her two sons. Could she have gone to America with them?
Hope this is of some help