Community Builder is using Joomla users table and API.

If Prestashop also uses Joomla's users table and API, then there is no reasons why it wouldn't be able to use existing registrations.

However, make sure that you continue to use Community Builder to register new users, as CB has a second table, #__comprofiler, for additional fields, that Joomla's registration will not handle. For that, it should be enough to make sure that the "Community Builder system plugin" joomla-plugin is activated, and that in its settings, "Redirect URLs" and
"Rewrite URLs" settings are enabled.

But now I plan to install Prestashop and it is not clear to me if a user of the Joomla+CB site will be able to login with his registration data.
For the moment, the basic fields are enough, I just want to avoid having to register again in Prestashop.

If it's a Joomla extension or has a Joomla extension for integrating with Joomla then it should work fine with existing users. It however looks like a completely standalone e-commerce solution that is not a part of the Joomla ecosystem. This means it will have its own registration and login process independent from Joomla.

Also, if they know of a better e-commerce option or one that goes more friendly with CB, I can take it into account.

Any that directly state they integrate with Joomla would be preferred otherwise you're going to have to bridge the two products yourself. You maybe able to bridge them at least from CB to your solution using CB Auto Actions (e.g. Query or Code actions to synchronize users to your solution).

I strongly suggest using extensions that are well integrated with Joomla, and at very least use Joomla's users-management API, so at very least have compatible users handling and compatible, secure, password-hashings.

Btw, if it's to sell few items, our own CB Paid Subscriptions allows that too:
www.joomlapolis.com/addons/cb-paid-subscriptions
It is not suited to sell many items, and does not have shopping-cart functionality (quantities>1, edition, and so on). But it has many nice features that shopping-carts don't have, and a seamless integration in Joomla and CB.