It depends on what you define as “googlefree”. If you just want to avoid Google Apps (Google Play etc.) then LineageOS might be ok for you. Also see Redirecting…, quote:
Google apps are the proprietary Google-branded applications that come pre-installed with most Android devices, such as the Play Store, Gmail, Maps, etc. Due to licensing restrictions, these apps cannot come pre-installed with LineageOS and must be installed separately. The Google apps are not required to boot or run LineageOS, however many users find them beneficial to take full advantage of the Android ecosystem.
And this image (source: Fairphone 2 - Fairphone Open — FAIRPHONE open source documentation):
LineageOS is mostly without the “Google Apps and Service” but still uses code from Google and some of their servers as explained (provisioning for eSIM, connectivity check, NTP, fallback DNS and SUPL).
But a complete free operating system like a pure Linux without any reference to anything from Google like PureOS does not exist for Fairphone 4 yet as far I know. Also keep in mind that the hardware needs drivers from Qualcomm and others and these are usually also not free software.
There was a discussion in the forum about PureOS in 2022 as well: Support for PureOS