Jan  4 11:43:45 sd-79356 postfix/qmgr[29420]: 374A1A4D72: from=<root@xxx.xxx.xxx.xxx.online.net>, size=361, nrcpt=1 (queue active)
Jan  4 11:43:45 sd-79356 postfix/smtp[29427]: 374A1A4D72: to=<xxxxxxxxxx@hotmail.fr>, relay=mx1.hotmail.com[65.54.188.94]:25, delay=0.67, delays=0.07/0/0.45/0.15, dsn=5.0.0, status=bounced (host mx1.hotmail.com$
Jan  4 11:43:45 sd-79356 postfix/smtp[29427]: 374A1A4D72: lost connection with mx1.hotmail.com[65.54.188.94] while sending RCPT TO
Jan  4 11:43:45 sd-79356 postfix/cleanup[29425]: DBBB1A4D75: message-id=<20160104104345.DBBB1A4D75@sd-xxxxx.dedibox.fr>
Jan  4 11:43:45 sd-79356 postfix/bounce[29428]: 374A1A4D72: sender non-delivery notification: DBBB1A4D75

smtpd_banner = $myhostname ESMTP $mail_name (Debian/GNU)
biff = no

append_dot_mydomain = no

readme_directory = no

# What I added to use TLS support, which doesn't solve the problem
smtpd_use_tls=yes
smtpd_tls_security = may
smtpd_tls_key_file = /etc/postfix/tls/smtpd.key
smtpd_tls_cert_file = /etc/postfix/tls/smtpd.crt
smtpd_tls_CAfile = /etc/postfix/tls/cacert.pem
smtpd_tls_loglevel = 1
smtpd_tls_received_header = yes
smtpd_tls_session_cache_timeout = 3600s
tls_random_source = dev:/dev/urandom
smtpd_tls_session_cache_database = btree:${data_directory}/smtpd_scache
smtp_tls_session_cache_database = btree:${data_directory}/smtp_scache
smtp_use_tls = yes
smtp_tls_security_level = may
smtp_tls_loglevel = 1
# till here

smtpd_relay_restrictions = permit_mynetworks permit_sasl_authenticated defer_unauth_destination
myhostname = sd-xxxxx.dedibox.fr
alias_maps = hash:/etc/aliases
alias_database = hash:/etc/aliases
myorigin = /etc/mailname
mydestination = xxx.xxx.xxx.xxx.online.net, sd-xxxxx.dedibox.fr, localhost.dedibox.fr, localhost
relayhost =
mynetworks = 127.0.0.0/8 [::ffff:127.0.0.0]/104 [::1]/128
mailbox_command = procmail -a "$EXTENSION"
mailbox_size_limit = 0
recipient_delimiter = +
inet_interfaces = loopback-only