I'm French.
Daycares are subsidized and operate on a sliding scale, but it can be challenging to get your kid into one, given logistics of work schedules. My single-mother cousin needed her parents to take care of her baby while she waited for a daycare spot close to either her parents' house or her workplace, so she could make drop-off and pick-up, because her parents couldn't do those. So it takes some finagling... but once you're in, daycares do not break the bank at all.
There is generous parental leave.
And health care costs are very low compared to here. My father was recently hospitalized for several weeks. Serious chronic diseases are 100% covered by insurance, so he doesn't need to pay for his medical treatments or pharmaceutical costs related to his disease, but he does need to pay the room and board fees at the hospital: 3000 euros for 3 WEEKs of hospital. I think here it would be 3000 dollars for a single day, no?
I know two college friends of mine who divorced soon after getting married. One had a kid. The number of paid days off compared to here do help parents figure out single parenting. Young kids often get sick, and here it can be a problem when you run out of leave, but in France that's not a problem. You have enough paid sick leave and vacation days to not worry about that.
OP, a word of advice: do not assume "Europe" is a monolithic block. Not all European countries are the same regarding daycare subsidies, parental leave and PTO. I've heard Germans have a problem with daycare costs and availability.