esp8266 client connect failed with cdn proxy

I have set an Arduino code (on an esp8266). The code is only doing the following :

• Set wifi
• Connect to a webserver
• Retrieve the html from this webserver and store it
• instantiate a server:port
• handle GET "/" request on local IP address and send back the html from the previous webserver.

Code is working fine (on 99%). I just need some support on the remaining 1%. :-)

1. When the webserver is having a "normal" IP address+domain name, the esp8266 can resolve it without any issue.
2. When the webserver is having only a "normal" IP address on the LAN, the esp8266 can get html from it without any issue.
3. But when this webserver is behind a CDN/Proxy activated (FYI this is Cloudflare), then the IP resolution is the IP from the CDN (seems OK) ; but the esp get an empty html or maybe a "0"... I'm not able to debug deeply on esp.

Is there anything I missed in my setting ? Any idea what should I try.

Thanks

I switched to BearSSL Arduino library to and some final point after getting SSL handshake Error 40. So in the end, I managed to use BearSSL and that solve the issue.