Well, I've never installed a language pack or worked with anything other than English, but I've looked at the fetch_phrase() function that decides which language to get a phrase from. It goes through them in a certain order and looks for the first language where the phrase is non-blank. So from what you describe it seems that it's finding the French before the 'Master" language, or else installing that language pack has somehow made French the 'Master' language. I think the master should be english that vbulletin comes with by default, so it should contain all phrases. But if someone or something has added phrases then Ozzy could be right. (Well, except that I still can't see why it wouldn't use the English if it exists in one of the other languages).
If you put your site in to debug mode (temporarily), the Master language should appear in the Language Manager. Maybe if you look at that it will provide some clues.
Here's an article on turning on debug mode if you haven't used it before:
https://vborg.vbsupport.ru/showthread.php?t=265999 .