Enniskillen was a town, a townland, a Parish and a Poor Law Union which covered up to 12 mi.
There are 16 James listed in the Griffith Valuation 1860
a census substitute. If father still alive he could of been one of these. Although they are from different Parish's all are in the PLU of Enniskillen.www.askaboutireland.ie
There are 13 Balfour's with two Parish's in common, Cleenish PLU Enniskillen and Kinawley Parish's.
In the current British telephone book for Northern Ireland there are 3 Bracken's living in Enniskillen and 8 Balfour's
all addresses come with postal code. I think it would be worth writing to these people with your information.
Gravestone inscriptions try www.from-ireland.net
and others. Local library may have Journals of inscriptions.
Looks like you have the parent material. Most Fermanagh
records don't go back early enough to have father James's and mother Catherine birth records but did you try for a marriage which would give you mother's maiden name?
Two resources for Northern Ireland:www.emeraldancestors.com
free to view & pay for recordwww.rootsireland.ie
pay website but not for profit Foundation