Yes Florence is a man's McCarthy first name.
It is the Anglicised form for Finn, Finnian, Fineen.
The Latin form is Florian.
Yes it is mostly a McCarthy Reagh name.
You will find that some of them are know as Finn & some as Florry or Flurry & many known by their middle name - common are Denis (Dennis) & John.
Other common 1st names in my McCarthy family are Justin, Cormac (Charles), Jeremiah (Jerry), Michael, Patrick, Donal (Donald).
My public tree is "Josephine Salt Familytree Halloween 2012".
Have a look & see if you can match any of your family.