Hello Susan, My name is Peter Callaghan and I have Family that came from Ireland. There is a Free Site called Irish Genealogy that has Information on Births,Deaths,Marriages,etc. If you have the Parish or County that Francis was Born in It would go a long way to being able to find Him. You also may get results from passenger Lists of People that arrived in America around that time.(1846 till 1873? Did he come to America by Himself or was He Married? If you can get any information on your G,G,G,Grandfather such as I have mentioned let me know and I'll see if I can Help.
All the Best