The desktop Firefox web browser has supported 128-bit on websites for ages as the Firefox Useragents used to have a U in UA to show it supported 128-bit however it was removed as of Firefox 4.0 because it was a obsolete thing to have in the UA since and no web browsers shipped with weak encryption support then.

https://www.ssllabs.com/ssltest/viewMyClient.html

What makes you think Firefox does not support 128-bit? as Firefox supports AES-256 since 2002 when it started out as Phoenix 0.1

See also:

• https://support.mozilla.org/en-US/kb/what-does-your-connection-is-not-secure-mean
• https://support.mozilla.org/en-US/kb/secure-connection-failed-firefox-did-not-connect
• https://support.mozilla.org/en-US/kb/troubleshoot-time-errors-secure-websites

Does Firefox offer 128-bit encryption? If yes, how do I get it?

I'm not sure whether we answered your question. If not, what do you want to encrypt?