Mental health treatment is usually not covered by basic health insurance, however many mutuelles do cover the costs for mental health treatment for children as a supplement. You need to check if your mutuelle does so and ask for the additional health coverage.
However, if 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