So I guess you would want to save their profiles : https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data So backup a profile.

So uninstall is first, never install with another version already on especially a real old one. Can install 2 but is not recommended due to the conflicts. Uninstall everything then Delete Mozilla Firefox Folders in C:\Program Files and C:\Program Files(x86) or with that age could just be Firefox.

C:\Users\<username>\AppData\Local\Mozilla this where the Profiles are stored. Unless all the installed files are there. Still try and remove with Add/Remove Programs first. If that fails rip it out.

Use Microsoft Disk Cleanup and or any other tools you would use. Then do your clean install. https://www.mozilla.org/en-US/firefox/organizations/all/

Please let us know if this solved your issue or if need further assistance.

I'm working on an enterprise solution for hundreds of computers. I need to automate the process of getting rid of older versions and then installing the latest version.

Does Mozilla provide any type of a solution for this scenario?

So should read : https://www.mozilla.org/en-US/firefox/organizations/ as should sign up for the mailing list and then get support through that. Plus there is the FAQ's

Might want to check answer in this Question : https://support.mozilla.org/en-US/questions/1170412

Deploying Firefox in an enterprise environment https://developer.mozilla.org/en-US/Firefox/Enterprise_deployment

As for uninstalling in mass..... This is old 2007 http://it.toolbox.com/blogs/locutus/remote-removal-upgrade-and-install-firefox-across-a-domain-17044

Might want to check here : Search terms used Firefox silent uninstall https://www.google.ca/search?q=Firefox+silent+uninstall&ie=utf-8&oe=utf-8&gws_rd=cr&dcr=0&ei=2NAEWuOPJs7CjwOirKDgBw

If that does not work, someone else may have the information for you. Will have to wait to see if get a answer.

Please let us know if this solved your issue or if need further assistance.