We are referring to girl's name here so why is it nor فَرَنْسِيّة?
The word اسم is masculine. That's why the adjective referring to that noun has to be masculine too.
Does this mean that she has a French name?
That's right why Francy and not Francieh
How do you say her name is فرنسي as in that's actually her name? Is there a difference between that sentence and what's presented in Arabic here?