From the Filezilla wiki FAQ:
How much does FileZilla cost?
Is FileZilla free?
Can FileZilla be used commercially?
FileZilla is free open-source software distributed under the terms of the GNU General Public License free of charge.
Basically this means that everyone, including corporate entities, can use FileZilla, including but not limited to private, educational and commercial use.
Notice the part about corporate entities. You are fine to install on as many PCs as you would like. Good luck!
