Saving preferred language for visitors?

Hi there,

i am looking for a solution for the following task (and i am wondering if this is possible with the language switcher):

i am using language switcher on the main menu on a big company website at a multisite network. I am using the multisites for the different translations / country representativs (about 7 multisites so far, on different sub-domains like de.website.com or us.website.com)

Now:
would it be possible to have the following feature:

A visitor is visiting the main page at the .com address (which is the global english speaking website) and is choosing his native language / country, let’s say: France.
He will be forwarded to fr.website.com.

Now, if he will come back at any later time, he should be autmatically forwarded to the last chosen language. In this example: fr.website.com

I guess, this has to be made with some help of cookies. But i am wondering what i need to have to get this function working and a) would it be possible to still use the language switcher plugin for multisites and b) would it be possible to use caching plugins and/or CDN Plugins (like KeyCDN).

I hope, i am at the right forum, but i just wanted to start my search here, because i am already using the language swichter plugin for over 1 year now…

thanks for any help or hints in advance!