This is incorrect. An Arduino library is a folder. That library folder must be installed under the libraries subfolder of the sketchbook folder.
So it would look something like this
<sketchbook folder>
|_ libraries
|_ FSM
|_ FSM.h
|_ <other library files...>
There is an alternative "recursive" library format that is actually more common than the "legacy" format shown above:
<sketchbook folder>
|_ libraries
|_ FSM
|_ library.properties
|_ src
|_ FSM.h
|_ <other library source files...>
Either format is likely fine for your application of a manual installation. I just didn't want you to be confused if you saw the different structure of some other recursive library you had installed.
Your #include directive is wrong. Change it to this:
#include <FSM.h>
The Arduino build system automatically discovers the library that contains the header file and compiles it. You should not specify the path to the file in your #include directive.