Making something available when it's not legal to do so is still a crime. Mozilla can't put the burden of "Is this illegal?" on the downloader. On top of that, with the specific nature of this law, they'll likely get added to this blocked list.
"For research" changes nothing, there isn't an exception for research in the French law (as far as I know, at least).
Nothing would stop a French person from taking extra steps to circumvent the law, so it's true that it could be gotten around with a VPN or peer-to-peer sharing of the installer, and Mozilla isn't liable for that, but also that would still dramatically reduce Firefox installs in France. It isn't really a good solution for Firefox to need the same steps as piracy for people to access it.
Firefox not needing user accounts isn't that relevant, because it's the distribution of illegal software that will be acted upon.
While it's true that they wouldn't necessarily have to pay a French fine, most large companies have assets in a lot of nations. For Mozilla, this could be people that translate the browser to French, who may have office space or supplies, and the French government could seize Mozilla's French assets, which also impacts their other projects like Thunderbird.
A search tells me they do have such an office in Paris which would be threatened by their noncompliance, which does include just telling French people it's illegal but letting them do it anyway.