Ok. So it finally worked for me for a few days, but today I tried to send a Pokémon to my game and nothing happened. When I click on "Test connexion" on my 3DS I see the following on the DNS Log:
192.168.1.4 has requested conntest.nintendo.wifi.net!
This is a valid request
192.168.1.4 has requested nncs1.app.nintendo.wifi.net!
Invalid Request! nncs1.app.nintendo.wifi.net