What do you think of the idea of introducing the user to all the features that Firefox has?
A kind of "did you know?" but intelligent and interactive, Firefox knows how to do such a thing.... and shows the user, if he accepts it, by highlighting the menu, the shortcut, the icon which allows you to do a thing, that he Do not know.
The thing that he doesn't know, that the browser might submit has to be done intelligently. It would have to be personalized. Consider a list of features that FireFox has where the user clicks on "I know" or "don't know", or "not interested". And according to these answers, he makes him discover one by one (each time he launches the browser) the functionality.
The user should have the possibility to silence the "did you know" notification, if ever, he was in a hurry, to come back to it later.
If the user knew all its features, he would be more inclined to use it and not another.