Firefox is not a SaaS. More so, it's Free Software so
you literally
own the program you run on your computer. You, the end user, are granted all the rights (well, except for the Firefox trademark) to do whatever you please with the binary or source code, under the MPL terms, essentially with the only restrictions imposed is that you have to do the same if you distribute it further (modified or verbatim).
If you legally need some license to type into a program on your computer (I don't think so, but let's say you do solely for the sake of imaginary argument) you can just give the license to yourself, no need to involve any third parties at any point here.
If Mozilla says they need a license so you can fill a form in Firefox, then they must've literally forgotten what Free Software even means. I hope this is not true, but merely a misunderstanding of some sort.