While I haven't tried it, cocos-2dx is, according to their documentation, is usable on Linux although my understanding is that this means one can build android projects using cocos2d on Linux.
In terms of where to start, I've used both SFML and SDL as both are well supported on Linux. Both are cross platform although SDL supports a wider range of platforms - I have an SDL2 game in progress that runs on Linux and android for instance whereas SFML does not yet have android or iOS support. Coming from cocos2d though I think you'll find the SFML API easiest to pick up.
As a fair warning, the landscape is a bit confusing at present because both SFML and SDL have a popular stable release (1.6 for SFML and 1.2 for SDL) with one API along side a popular development release (2.0 for SFML and 1.3/2.0 for SDL) that has a similar but not identical API. This is particularly noticeable with SDL where the documentation for 1.2 is much better than the documentation for the development API. In terms of choosing one over the other, the stable releases are precisely that - stable. In both cases the development releases have been under way for some time so if you are willing to dig for documentation a bit and ask questions it's worth getting the new features.
There is book that provides a nice introduction to Linux game development that, while dated, might be a good first step if this is your first outing with games on Linux, especially if you decide to use SDL Programming Linux Games.
Update:
I saw the directions here and after (roughly) following them cocos2dx does build on my Ubuntu 12.04 x64 machine. The "Set up Environment" directions seem sound but the makefile information appears to be out of date as there is no build_linux.sh instead there is a make-all-linux-project.sh. After this finished pulling in missing deps and building I changed into the samples/HelloCpp/proj.linux directory and ran make. This created a HelloCpp binary in samples/HelloCpp/proj.linux/bin/debug. Running that popped a HelloWorld cocos2d screen. According to the output the verison is:
cocos2d-x debug info [cocos2d: cocos2d-2.1beta3-x-2.1.0]
That said, I don't see a lot of documentation for the linux port and most of the related community entries seem to be out of date so you may find more support from using one of the libraries I already mentioned.