The most common description of au pair duties that you find on the web say 2 evenings of babysitting, with at least 2 whole days off without any babysitting; if Saturday is a normal workday for them, then you should give them at least one Saturday evening per month free of babysitting duties.
My view is that if you want to go out most Saturdays, then you should make their days off Sunday and Monday. If this won't work, then pay them to babysit - it should be a lot cheaper than hiring an outside babysitter because you only really need to pay up to about 10 o'clock, even if you are rolling home after midnight.
Depending on where you live, an au pair job can be really dull and lonely and a lot of girls really look forwards to the weekend when they can meet up with their friends and do young-people type activities. I think they need an incentive to work Saturdays, like extra pay and maybe letting them invite one of their friends over to keep them company. OTOH, it's not reasonable for them to never work Saturdays (paid), so if they are inflexible, they risk the heave-ho.
You can budget into your au pair costs the price of Saturday babysitting - you can pay them slightly less than you might for their normal duties and make it up with the Saturday payment. For example, if your instinct is to pay £70 a week, so pay them £60 and £10 for Saturday night.
I know that they agree to terms and conditions up front, but I don't think many au pairs know what they are getting themselves into and their main objective at the time is to secure the job - they'll say yes to anything, it seems. If you hold them to this, then you will have a grumpy au pair in no time and a horrible atmosphere in your house.