crèche seems to be used in British English
US English seems to prefer daycare centre
Flexitime is often used for work rather than for the care provider
The meaning in French is explained on the website below.
It basically means open on a short-term or long-term basis, either regular hours or an hour here or there.

Another slant: with no context cannot tell if it is 'special needs'or even providing different activities. 'Inclusive' is used for schools that cater to children of all abilities/disabilities.

cchat's link is convincing. In this case I can only find the slightly laborious description above on English speaking crèche sites, e.g.

"Opening Hours

The creche is open from 8:00am until 6:00pm for full-day care.

Those partaking of half-day care would stay for five hours depending on the requirements of parents and prior arrangements. These hours tend to be from 9:00am until 2:00pm. However due to the ratio required for younger children we only provide part-time care for children of 2½ years or older.

All full-day children from the ages of 2½ years to five attend the playgroup montessori from the hours of 9:30 until 12:00am. There are limited places available for the playgroup/ montessori.

We provide after-school care care and collection service for St. Pius National School, Terenure and Bishop Shanahan National School, Templeogue. We also provide full day care for our afterschool children during the holiday periods using our bus to take excursions. We are open to discussing any after-school needs a parent may have.