Florence, from Latin "flourishing", was originally a male name, as Florentius. This was used in old documents in Latin. Florence became almost always used as female name sometime after the early 19th century.
There is a record of a "Florence McCarthy" - male, born in Ireland - working as a Coast Guard in Fraserburgh, Scotland in 1841. A correspondent [GB] noted on a gravestone that, in 1838, he buried his son, James, in Freaserburgh. A private correspondent [MS] has discovered this usage in south-west Ireland at least up to the end of the 19th century.
The Gaelic male name Fínín was Anglicized as Florence in the Middle Ages. Autocratic British rule forbad the use of Gaelic names in the 18th century and several variants of Fínín were 'converted' to Florence. Examples include Fínn, Fínían, Fíneen & Fyneen.