The Nokia 6120 is over 15 years old and was never designed for modern apps. For security and practicality, I strongly recommend using a modern smartphone (even a low-end Android or used iPhone) if you need Facebook Messenger.
Several archive sites host the specific versions required for the Nokia 6120 Classic free download facebook messenger for nokia 6120
: Many modern websites, including the standard Messenger.com, may not load correctly on the Nokia 6120's browser due to outdated security certificates and lack of support for modern web standards. Download or update your Messenger app The Nokia 6120 is over 15 years old
Install an old version of Opera Mini (you can still find .jar files online). It compresses data and might make the Facebook mobile site slightly more usable. including the standard Messenger.com