If you make the source code available, people will install the program in whatever way is the standard on their distribution.
There are various formats of packages which contain your program, its data and its dependencies. When the user installs the package, the package automatically ensure that the dependencies are installed as well.
You just give people the source code, the data and the installation instructions, and if your program gets somewhat popular, some people will create the packages for their distribution.
If you don't distribute your source code, you can create an installer (can be as simple as a script or can be like a Windows installer) which will attempt to install the program à la Windows. That's pretty ugly though.
Also, what says you can't take the shared libraries of Linux and put them in the same folder just as Windows? Works there too. If you are having trouble finding your SFML library files then they should be placed under /usr/lib and just search after "sfml".
If I remember correctly, you can't do that because of security issues. I just tried it and it didn't seem to work, but it's been a while since I made a so so I might have done something wrong.