Important to know
The name "animal care center" is a little misleading. If you think of a loving environment for your four-legged friend at an "animal care center", then this probably applies to many facilities. At Disneyland Paris, however, this applies only to a limited extent. The cast members who work there are very animal-friendly, but the facility itself is not particularly inviting. It is a collection of kennels and enclosures that are completely bare. If you don't bring a blanket or basket, your dog will spend the time there on the tiles or on a steel surface (depending on the kennel).
You should be aware that staying in this facility means pure stress for most animals, since many animals (some of them being fearful) are close together and have nothing to play with or to run. If you have another way to accommodate your pet, this is certainly the better choice. So its better to search for a nice place for your dog or cat before your trip to Disneyland. Surely there are nice neighbors, someone in the family or friends, maybe also a nice animal pension in your area?