You can install annoy-o-tron monitoring software (like Tiger), or even copy the scripts from your FreeBSD system (/etc/periodic/{daily,weekly,monthly,security}/*
and the periodic
script itself in /usr/sbin
) and modify/run them on your Debian box if you really want to, but this is a bad idea.
The periodic emails on FreeBSD are a TERRIBLE monitoring solution - they are almost entirely noise (messages requiring no action) and train you to ignore the monitoring messages because you typically don't need to do anything when you receive them.
A better solution would be to look at implementing a real monitoring system which only sends you alerts when something actually requires your attention.
You can then turn off the annoying periodic emails from your FreeBSD systems (I typically send them to /var/log/periodic.log
in case I ever want to see the output), and enjoy the bliss of not having your inbox filled with email that doesn't really require your attention.