It's become a common way of signaling that your app/service is "Free as in Freedom", as opposed to "Free as in beer", open source vs. FOSS, etc.
I find it a little odd here, because Firefox already meets the definition of FOSS. But it's not unheard of for a popular project to go from free to proprietary, and for a fork of the last free version to somewhere work "libre" into the title.
More to the point, "Librefox" is a project about privacy, not freedom. Others have pointed out that this project actually bundles some proprietary addons—so the name makes no sense.
It's become a very effective way for me to detect projects that have prioritized idealism over pragmatism. (I personally fall on the pragmatism side of that spectrum, and so I find it useful to avoid the oil-water problems that causes.)
Which always irks me, because we already have a great word to mean "Free as in Freedom", and that is: "Freedom."
I'd love if we could start calling free software, Freedom Software. Think of the benefits to the FLOSS PR movement!
I actually e-mailed rms about this, he said they considered the name but couldn't use it because of a trademark. I say to hell with that: the needs of the many, and all that! Freedom Software for all!
I'd just like to interject for a moment. What you're referring to as FOSS, is in fact FLOSS, or as I've recently taken to calling it F/L/OS/S meaning “Free/Libre and Open Source Software”. Free is not free by itself, call if F/L/OS/S to explicitly avoid a preference between the two political camps. If you wish to be neutral, this is a good way to do it, since this makes the names of the two camps equally prominent.
There really is a F/L/OS software and there are people who use it, but it is just a part of the system they use, that in fact called GNU/Linux. Anyway Libre refers to freedom, instead of calling it open source you could also start to call this type of software Libre software. “Free and Open Source Software” is misleading since it can be interpreted as free as in beer when it is Free as in Freedom. Not calling it FLOSS is an obstacle to understanding GNU philosophy, free software and open source are different political positions that are completely not the same.
So, I would assume that the French pronunciation is the intended one. Although I might be wrong.
Of course, the author has used the name "Librefox" as a single word, so there would presumably be liaison between the "e" and the "f", and so therefore you would presumably actually hear the "e" in the French pronunciation.
Even now people everywhere have problems pronouncing GNU, Emacs, or Linux, and the word's connection to "liberty" should become clear if someone thinks about it for any time. Both "free" and "open" have their own problems, it seems like a fine alternative.