In SharePoint 2007, you can't change the actual language of the current site, so it would never be applied. If you are using a tool like IceFire, it handles only some of the site content, and not the settings like this one.
In SharePoint 2010, you would probably be able to activate the MUI and set the Group name in english when you are viewing the english version of the page, and set the name in french if you are using the french version of the page. The MUI keeps track of the localized strings. The only thing I'm not actually sure is if the groups settings are actually used as data or as settings. If they are used as data, you won't be able to use the MUI features.
But, there is also the question : Why would you need 2 versions of a back-end value ? You should make a corporate choice to go french or english. Those values are almost never displayed, which makes the localized versions a bit useless...