Maternity Leave/Pay After End of Fixed-Term Contract

onyxx wrote:

I understand I will get statutory maternity pay for 6 weeks prior and 8 weeks after birth, and then my employer would normally pay 65% of my normal salary for up to a year after birth.

The fist part of your statement is correct: Your employer will pay your full salary from six weeks before the calculated birth date to eight weeks after the actual birth.
But they will NOT pay anything beyond that!
You are probably eligible for "Elterngeld", which is paid for another 10 (in some cases 12) months after that and amounts to 65-67% of your previous (after-tax) income, subject to a min. of €300 and a max. of €1800/month. This comes from the government and you need to apply at your local "Elterngeldstelle".
You can also get "Kindergeld", which is paid until the child becomes an adult and is currently €204/month. You need to apply for this at your local "Arbeitsamt".
You can get "Arbeitslosengeld" (unemployment benefits) only if you are available to (and looking for) work, which you say you are not. In that case, you can only get "HartzIV" if you are destitute (i.e. have no savings or other means to tide you over the period).