When I desactivate wpforo plugin, it's working perfectly. I checked in the settings what could be related to this but I couldn't find anything enabled that would explain that.

Yes, that's something strange, we don't see such problem in our test website and here on wpForo community. The Edit button goes to WP Profile Edit page. Please try to deactivate wpForo (not uninstall) then delete all caches and activate it again. Also try to deactivate other plugins, maybe this is a plugin conflict.

Problem is gone, and I have no clue why. 🙂

And problem is back. I still don't know why ! I didn't activate or desactivate any plugin since yesterday...

wpForo is not designed to replace User and Customer edit URLs to forum profile URLs by default. It doesn't replace on all our test sites. I think this is a site specific hook priority  or a plugin conflict issue. We've made some change in core of next release to prevent such cases. But for current version you can do a small change in /wpforo/wpf-includes/wpf-hooks.php file.

Find this line:

add_filter( 'edit_profile_url', 'wpforo_change_default_edit_user_page', 10, 3 );

Replace to this:

//add_filter( 'edit_profile_url', 'wpforo_change_default_edit_user_page', 10, 3 );