Maternity leave/FMLA

I’m a teacher and will be meeting with my principal this week about maternity leave. My main concern is making the most of what leave I am offered. I know I get 12 weeks through FMLA. my school does not offer any additional time off paid or unpaid. I also have short term disability. We recently received our contracts for next year: 10 month contract going from August through May and get payed over 12 months. My questions is does FMLA start when I have the baby (due July 2) or when my contract starts August 1st? I plan on asking all of these questions to our HR/finance and benefits department but don’t have 100% confidence in them getting it right. Any info welcome! Thanks!