For foreign readers, the income tax in France is a secondary tax that more than half of workers do not pay at all (it's low compared to other taxes and it's divided by the number of children). Don't be mislead when hearing that there is no income tax, France has many taxes.

What you say is misleading. (1) That's not quite right for a single parent because they get more allowance but can't claim tax credit with no tax. (2) That's not quite right for a couple each around minimum wage because they get no allowance but may claim some tax back. (3) That's not quite right for a couple with good dual income or extra revenues because they're not eligible to any benefits but may be able to claim a good chunk of the child care in tax credit.

France has extremely strong threshold effects. A penny less and there's more allowance, a penny more and benefits are cut while taxes are increased. It's really hard to generalize.

In all cases though, it's tough for a household to pay for childcare. My sister is a childcare worker so I'd know, all parents are dual income earners, like the equivalent of the high earning engineer/lawyer household making $300k+ a year in the valley. They earn enough to pay for childcare upfront and get a fair chunk back in tax credits.