I’m afraid your post doesn’t give us enough information to offer much assistance.
I was able to deduce that your site uses (or has used?) Cloudflare. So this can make it much more complicated to diagnose, your screenshot doesn’t even show the certificates presented or provide any details of what the problem was, just an error message in French. So i doubt anybody will be able to help much without more information from you, sorry.
The site has used Cloudflare on my other host, I have change for 2 weeks ago.
My new host can install the Let’s Encrypt certificat when I press a link, it’s automatic and works perfectly on Firefox and Google Chrome.
I had think that Let’s Encrypt doesn’t works on IE 6-7 (Windows XP) but my problem is very strange.
The message explain that “The certificate on this website has expired or is invalid.”.
That’s a very generic error message. Does clicking on “Informations” show any additional details? Can you test your site using SSL Labs and share the results?
Some additional details: The certificate is only a very small part of what determines browser compatibility. More relevant is your server configuration, especially the supported protocols and cipher suite.