Hi Nicolas and everyone else!
As mentioned above, you can do this with the free version of Beaver Builder! We're 100% GPL, so you don't need to worry about selling the theme on your site, too.
We actually wrote an article that explains some of the best practices of including Beaver Builder in a theme:
One of the big takeaways from that article is that you do not want to bundle the plugin with your theme, but use a plugin like TGM Plugin Activation to do it for you:
This is the "proper" way to include a plugin with a theme since this plugin encourages the user to install the plugin. Then, they'll be responsible for keeping it updated. This is how Webman Themes and UpThemes are integrating Beaver Builder with their themes.
Another cool feature with Beaver Builder is that you can add an affiliate tracking id to the upgrade button in the page builder. If anyone upgrades Beaver Builder after using it in your themes, you get a 25% commission!
Hope that helps. Feel free to contact me privately to discuss, too! I am always happy to chat page builders..
robby [at] fastlinemedia [dot] com