I addressed your speculative question to a very old family friend who was born in that area, albeit Creeslough.
His fairly instant response was either (1) The Inniskilling Fusillers or (2) The Connaught Rangers. He joined 'The Skins' but some of his boyhood friends had gone for the latter in the choice of infantry units.
Royal Ulster Rifles was the re-named Royal Irish Rifles after the partition of Ireland, they then went on to fight in WW2 and Korea.
The Royal Inniskilling Fusiliers would have recruited from Donegal during WW1
Philip Orr's book "The Road to the Somme" tells us that the Donegal and Fermanagh Volunteers (based on the structure of the UVF) became the 11th Bn Royal Inniskilling Fusiliers, and that the Derry Volunteers became the 10th Bn Royal Inniskilling Fusiliers. There were also the 6th Royal Inniskilling Dragoons, and a variety of support units (Field Ambulance, Signals, Service Corps) which he might have joined.
Of course if your young ancestor had been Roman Catholic he might have joined one of the regiments supported by William Redmond's Irish Volunteers. Connaught's, Leinster's, Dublin's, Royal Irish Fusiliers, and others.
The bulk of the Royal Irish Rifles were from Belfast and east Ulster - Antrim and Down).
He would have been welcome anywhere, brave men all!
And by the way do not call them Enniskillens, or even Inniskillens: they are Inniskillings!
As an aside to this my recent research into the names on my local war memorial lists three pairs of brothers who did not return. Two of these pairs were cousins. Two other brothers of one of these families also served but returned safely. Think of the anguish and torment of the parents and siblings in what was then a close and intimate community.