Le site libressl.org est-il sûr ?

It's a fork of OpenSSL made at least in part due to the Heartbleed bug, as indicated by the site's favicon. I cannot give it full green as this has caused fragmentation in the SSL toolkit market - LibreSSL supports ChaCha20-poly1305 while OpenSSL only supports it in version 1.1.0 which has poor adoption due to an updated, incompatible API. OpenSSL 1.0.2 and greater support multiple certificates (for example dual-stack RSA/ECDSA) in nginx, as of the last version I tried of LibreSSL it doesn't support the feature. For me, the lack of ChaCha20 support in OpenSSL 1.0.2 isn't as bad as LibreSSL's lack of dual certificate support.