I'm sorry if the title is a bit weird, but it's pretty hard to actually describe this weird bug.
What I mean by the language file that loads alternatively, is that everytime I "refresh" any page on my blog, the language will either be set in french or in english, seemingly at random. Take a look at http://www.monamouchtim.com/ , and refresh the page a few times. You will notice that the date for the posts switch from french to english every few refreshes (goes from "Friday" to "Vendredi". In the admin it's the whole interface that changes since most values are generated, whereas the main page is mostly all static text...
The only thing that I've done different from a "standard" installation is that I installed the full french translation of wordpress 126.96.36.199 (on the WordPress Localization Codex page), available here. I have not changed anything in the script except the theme (I added some things in the sidebar, modified the header... aesthetic changes only), and added the author.php page.
Can anyone tell me what's happening, and how I can fix it?