From my experience, the following domain registrars provide free email hosting for user's domains.
They have the email hosting with good reputation. Easy setup, solid systems.
Every domain can get two mailboxes for free, each with 3GB as storage. Webmail has Roundcube, Sogo for choice.
Gandi's price is not cheap, for instance, the .eu domain wants 15 EUR/y from them, while most others are about 5 EUR/y.
They have one mailbox free for each domain registered in them.
The email is powered by open-xchange, which has better experience in webmail system.
Their price is not cheap though.
This is a germany domain registrar, providing cheap price for .de domains.
Every domain with them gets a free mailbox, with Roundcube webmail.
But you can't change the email username, it's "postmaster" by default.
Their domain admin panel is hard to use.
OVH has a lot of cheap domains. Every domain can get a mailbox for free.
Their admin panel is hard to use. And you can't change the username for email, it's a default contact address.
Webmail is the old version of Roundcube which I don't suggest to use.
Every domain with them can get a mailbox for free.
It's 1GB in size, powered by Roundcube webmail. The domain has also a free 250MB web space included.
Their new domain panel is much better than the older one.