If your recipient is not registered on Peppol, the Peppol button won't turn green and you won't be able to send your invoice.
You can also send e-invoices to public entities via Chorus Pro. For that, you need the SIRET number of your recipient, which you can find in this database.
After adding the SIRET number of your recipient, you can send your invoice via the button 'Send to Chorus'.