I recently told my HR department that I was going to take paternal leave for the birth of my child. I have over 900 hours of sick time, and 400 hours of vacation time saved up. I am planning on using that time for my leave. When we first found out that we were going to have the child, I went to my supervisor and told him that I was wanting to use the 6 weeks that I get off every year as my time for paternal leave and he agreed to it. Now HR is saying that they are counting this time toward my FMLA even though it was originally scheduled to be my vacation. Can this be done...

Yes. Your employer is free to designate any absence time that qualifies for FMLA leave as FMLA. In many instances if the employer fails to do that, even if the employee has not applied for FMLA, the employer could easily be in hot water.

Your FMLA leave will run concurrent with your paid vacation. (FYI, the Act allows the employer to require an employee on FMLA to use any paid time off - vacation, sick days, personal days - concurrent with FMLA time.)