Mental health treatment is usually not covered by basic health insurance, however many mutuelles do cover the costs for mental health treatment for children. You need to check if your mutuelle does so and ask for the additional health coverage.
However, when you choose to go to a private hospital, all costs may not be covered by insurance.
For more information: https://www.bfp-fbp.be/fr/remboursement-par-des-mutualites