Can't update plugins after enabling SSL.

Hey there,

Self hosted here, Debian 8.3 x64, Apache2, PHP5, MySQL, a basic LAMP server in the end.

I’m migrating servers, and as i’m hosting quite a few sensitive stuff, wanna switch to SSL (HTTPS).
So i just got my (first) authority signed SSL certificate to work right.
Changed default page from http to HTTPS, corrected some links, everything’ is perfect about that.
Except now i can’t update or install plugins. I’m pretty sure it’s be the same for WordPress updates.
So i’ve been googleing for around an hour, without finding a satisfying solution. Feels like i’m the only one having this issue…

So here is what i get :

Screenshot : http://image.noelshack.com/fichiers/2016/13/1459473572-update-plugins-fail.png

Downloading update from http://downloads.wordpress.org/plugin/buddypress.2.5.2.zip…
An error occurred while updating BuddyPress: Download failed. The SSL certificate for the host could not be verified.

My Apache logs floods that :
[Fri Mar 25 12:55:00.200119 2011] [:error] [pid 3589] [client xx.xxx.xxx.xx:54872] PHP Warning: An unexpected error occurred. Something may be wrong with WordPress.org or this server’s configuration. If you continue to have problems, please try the <a href="https://wordpress.org/support/">support forums</a>. (WordPress could not establish a secure connection to WordPress.org. Please contact your server administrator.) in /home/terageek/www/wp-includes/update.php on line 467, referer: https://www.terageek.org/wp-admin/update-core.php?action=do-plugin-upgrade

Do you guys have any idea ? Because i’m totally stuck right now.
Thanks for your attention.