Do you have an employment contract? If so - get it out and see what restrictions you have. If not, you are likely an at will employee and can leave at any time with reasonable notice. The FMLA has nothing to do with your rights --- is it paid FMLA leave? Or Unpaid? You may want to offer some of the money back if paid.
I would also encourage you to call a local employment attorney as every state has different laws on employment rights and restrictions.
Good luck - and Happy New Year