I've read that Firefox now supports DRM, but I don't know if it's already on Ubuntu, do you know if it works? Thanks.
As others have noted, Netflix won't play in the Linux version of Firefox 48.
But Netflix can be played in the Linux version of Firefox 49, which is currently in beta, and can be installed from ppa:mozillateam/firefox-next.
Once Firefox 49 is installed, you'll need to be certain that the Widevine plugin is installed and activated. (It wasn't installed/activated by default for me.) Also, because Netflix doesn't yet officially support playback on the Linux version Firefox, at least for now, you'll need to use a "User Agent Switcher" set to reflect a recent Linux version of Chrome.
You can find more information here: http://www.ghacks.net/2016/08/13/firefox-49-linux-netflix-amazon-video/
For what it's worth, at least for me, Netflix currently plays better in Chrome than in Firefox. But Firefox 49 is still in beta, so maybe things will improve.
I just tried to stream Netflix on my Ubuntu 16.04 machine with Firefox 48.
The site itself works fine, but once I try to start a stream, Netflix asks me to install the Silverlight plugin, which, of course is Windows only.
So no, it doesn't seem possible to watch Netflix on Ubuntu with Firefox. If you do buy the service, you'll have to use Chrome (Chromium doesn't work).