How can I choose a different client certificate in Firefox?

You need to clear SSL session state of your browser. Take a look at my anwer to a similar question:

in Firefox choose History -> Clear Recent History... and then select "Active Logins" and click "Clear Now".

The most straightforward way to indicate Firefox that you want to be asked every time for the right certificate is to adjust the security.default_personal_cert property in "Advanced Preferences". I have not found a way to do it through the "Options" menu, which is the recommended and safe way to change your Firefox preferences.

How to proceed:

1. Access Firefox's "Advanced Preferences" by opening a new tab and typing about:config into the address bar
2. Firefox will display a "Proceed with caution" warning. Click on "Accept the risk and continue".
3. On the "Search preference name" bar, type security.default_personal_cert
4. Set the value of that property to Ask Every Time
5. Close the tab (make sure that you do not change anything else)

You are done. If a website needs a certificate, you will now be asked to choose one from the list instead of having it automatically selected.

(Note: I am using Firefox 85.0 (64-bit) on Windows 10. If I am not wrong, previous versions of Firefox allowed to change that preference from "Options".)

With the selected answer (2015), you clear "all data since the last XXXX hours". Nevertheless, as per this answer (2020) from @Luke https://stackoverflow.com/a/65303926/1315009 you can pick what decissions to remove, site per site.

Settings > Privacy & Security > Security > View Certificates... > Tab Authentication Decisions => Pick from the list and delete.

Tested on Firefox v102.0.1 & v103.0.2 and it works.

hint

Inside settings type cert in the search and you get there in a split-second: