Whether you need to pay for the holiday will depend on your company's policies and practices with respect to other forms of unpaid leave. Specifically, your company needs to treat unpaid FMLA leave no less favorably than it treats other forms of unpaid leave. If employees at your company who are on unpaid leave for non-FMLA reasons are paid for intervening holidays, then so should employees who are on unpaid FMLA leave.
The applicable U.S. Department of Labor regulation provides as follows: "An employee's entitlement to benefits other than group health benefits during a period of FMLA leave (e.g., holiday pay) is to be determined by the employer's established policy for providing such benefits when the employee is on other forms of leave (paid or unpaid, as appropriate)."
Your company's FMLA and other leave policies should be clear on whether intervening holidays will be paid. It is always a good idea to have qualified employment or benefits counsel review all company policies regarding paid and unpaid leave, not just FMLA leave policies.
Source: 29 C.F.R. §825.209(h).