No, Firefox allows you to rebrand modifications and so is Free Software. If it enforced that you keep the branding, that would be non-free.

Here it is right in the list of APPROVED Free Software licenses: https://www.gnu.org/licenses/license-list.html#MPL-2.0

You're talking semantics. Sure, the branding is non-free (you can't distribute the same version obviously), but your four freedoms aren't diminished in any way [1].

[1]: http://www.gnu.org/philosophy/free-sw.html

Firefox is non-free due to trademark protection, but that's VASTLY different to being non-free due to being a paid download, or being closed source, or patent licensing, or restrictive licensing terms, and so on. It's almost irrelevant to the parent poster's comment to claim that.