The standard release of FullCalendar is released under the MIT License, which puts almost no restrictions on how you can use it. You can even freely use it in a commercial project. The only stipulation is that you leave the copyright header at the top of each file intact. This is the same license that the jQuery project uses.
The FullCalendar Scheduler add-on is released under different licensing terms than the standard edition of Fullcalendar. There are more restrictions on how it can be used.