I am working on a website through Wordpress using Classipress theme. I’m having a weird issue, where the home page I want to display is only displayed when a user is connected. When a user is not, there is a strange “blog” page, which is, I guess, from the home.php file.
Please find below the two situations :
User connected and homepage (the one i always want):
anybody can help？ 
I’m afraid that you’re in the wrong place. This is a forum about ClassicPress, which is a CMS or website-building platform originally forked from WordPress.
You are looking for the home of ClassiPress (note the spelling without the middle c), which is a theme for WordPress.
It might be that you could switch your site from using WordPress to ClassicPress, and we’d certainly be happy to help if you decide to do that. But it wouldn’t address your immediate problem.
You need to go back to where you obtained your theme and ask for help there.