Honestly, I can't really say we are doing anything to plan financially, other than maybe buying a new car soon so that I don't have to worry about mine dying while I'm on mat leave (it's secondhand and we pay cash, so no payments). If you can manage your basic expenses on your maternity leave income level, you should be fine. Babies really don't cost much. What a lot of people spend money on when they have a baby are things they want, not things they need. They don't need loads of outfits or shoes (they don't need any shoes). They don't need fancy decorated nurseries. They don't need a new toy every week (you'll be amazed that random junk you find around your house, like a colander or some pine cones or some sand, will be much more fun than some toy you spent lots of money on). Their needs are pretty basic.
I also felt like I saved a lot of money not doing things I would have done before we had our daughter. Like, you don't really have much time to go for a night out or a romantic meal at a nice restaurant, so we saved loads on all those bar tabs and meals out we used to have. I also didn't have commuting costs for work anymore, so no petrol, parking, train travel, etc. We tried to do lots more free things, like rather than signing up for some expensive baby class, we went to the library or the park or the beach on months when things were a bit tight.
We also tried to get rid of unnecessary expenses. We don't have car payments, and we keep our tv, phone, internet bills low. We don't have pets or gym memberships or other luxuries like that. We really just focused on having the basics and what we really needed. My mat pay covers our rent, so my husband's salary can pay anything else. Having a little cushion in the bank is a good idea, in case, god forbid, your car breaks or you have a house repair or other emergency expense, but I don't think you have to go crazy. If one or both of you can take on extra work now, or in his case, once baby arrives and you are settled and feel like you are managing well on your own, then in the long run, it will mean you can have more time at home and save on child care expenses. The most expensive thing I think about having a baby is child care once you go back to work, so if you can stretch your leave as long as possible to save on that, do it. You'll save money and get more time together.