Once you update nameservers for a .it domain, the .it registry will check for validation of the nameservers you have updated. If the nameservers do not pass the validation, then they are rejected. So, please contact your webhost, and request them to check if your domain is added correctly with them.
Also, please ask them to check if the zone file for the domain is setup with correct NS and SOA records. Once this is done, please update the nameservers again and your domain will work fine.
Note: You may need to check the validation status at the registry if their websites provide the options.
For .IT domains the Validation status URL is: http://dns-check.nic.it/
For .De domain: URL https://www.denic.de/en/service/tools/nast/
For .FR domains: http://www.afnic.fr/fr/produits-et-services/services/zonecheck/