I research the Irish Family History Foundation's database. It contains 12,800,000 surviving rcds for abt 70% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800. Cos. Donegal and Derry were recently added to the database.
Note 1 - Without a KNOWN county, the chance of an ancestor's rcds NOT being in this database is AT LEAST 30%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
For James Breen B ????, Co. Louth, with a father forenamed "Bart," I found 1 rcd in 1858. This doesn't fit your parameters. Your stated 1866 DOB is consistent with the general immigration pattern for Irish Males: immigrate between ages of 16 and 24. It appears his B rcd didn't survive.
For Bart(holomew) Breen M ????, somewhere in Ireland, I found 1 rcd in 1866 Longford. This Co. is near Louth.
For Cat(herine) Finnegan M 1866, Co. Longford, I found 0 rcds. This is a NO match. It suggests the rcd for Bart is a false positive.
B/M/D rcds for Co. Louth are only for RCs. Civil and other denomination's rcds don't exist, or haven't been transcribed yet. Suggest you wait until they are.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.