Does Laravel regenerate the Session ID? (compared to CodeIgniter)
Like pstephan1187 noted, "Laravel only regenerates the session ID when you sign in and sign out". CSRF Protection is used against cross-site request forgeries, and it consists of a field that is required by default (Laravel 5) in POST, PUT and DELETE requests.
Handling this in ajax-calls is outside the functionality offered by Laravel, but can be worked around pretty easily.
For more information about Laravel sessions, see the official documentation (Which, by the way, is a very nice and easy-to-understand read).