As I view your line, and not knowing your age, your third or fourth line should have a William Finucane to be in our direct line.The relation would have to go back to John Finucane/Johanna Brown via Micheal to make a connection.
If you saw a post of mine regarding a Coat of Arms, it was me debunking it.Several Finucanes boast about having one, but the fact is the Finucanes do not have a coat of arms.
Since 1552, the usage and granting of coat of arms has been strictly regulated by the Government of Ireland, through the Office of the Chief Herald of Ireland.
The "Finucane" coat did not appear until the 1800's during an era when geneology became popular in the states as people tried to reach back and recreate their family histories.An industry was born and still exists today where people create them and sell them as authentic.
That said, a cousin of mine who did originally post about it, changed ours to reflect the comical side of our immediate clan!