Okay the problem is now fixed. Huge mistake from my side : the email from Admin → settings → notification email was not the same from the smtp username.
Maybe a check should be made to prevent user to makes this mistake 
but it seems like DISCOURSE_SMTP_AUTHENTICATION: login isn’t required
True, the final config
DISCOURSE_SMTP_ADDRESS: smtp.office365.com
DISCOURSE_SMTP_PORT: 587
DISCOURSE_SMTP_USER_NAME: test@example.fr
DISCOURSE_SMTP_PASSWORD: password
DISCOURSE_SMTP_AUTHENTICATION: login
DISCOURSE_SMTP_ENABLE_START_TLS: true