Is this library a public library? I went here and a woman told me there’s a monthly fee.

Hello! This is a location of Jacksonville Public Library, free to residents of Duval County and many others (DCPS students, military and their families, college/university students in Duval County, those who teach (any school or homeschool) in Duval County). For those who don't qualify for a free card there are quarterly and annual memberships available for $25/quarter. Might that have been what the staff member was talking about?

There is a fee if you don't live in Duval County.