As translating custom post types seems to be a pro feature of the Polylang plugin, it should be compatible with the Content Blocks plugin.
Unfortunately the option is greyed out for me so I cannot test it myself:
If it doesn’t work you can use WPML, which has been thoroughly tested with the Content Blocks plugin.
So the reason that section is greyed out is that Polylang isn’t recognizing the content blocks as custom post types. I tried installing a different content block plugin (Reusable Content & Text Blocks by Loomisoft) and the section is active, and allows me to enable Polylang.
Polylang is a great alternative to WPML because its free version is suitable for most applications. WPML free is limited to 2000 words, which is very restrictive.
I tried this, but it did not work. Thanks for trying though. I would love to use your plugin as it is well-supported compared to other content block plugins.