If you're using JNA you probably want to explicitly specify the values of the enumeration in Java. By default, Java's basic enum type doesn't really give you that functionality, you have to add a constructor for an EnumSet (see this and this).
A simple way to encode C enumerations is to use public static final const ints wrapped in a class with the same name as the enum. You get most of the functionality you'd get from a Java enum but slightly less overhead to assign values.
Some good JNA examples, including the snippets below (which were copied) are available here.
Suppose your C code looks like:
enum Values {
First,
Second,
Last
};
Then the Java looks like:
public static interface Values {
public static final int First = 0;
public static final int Second = 1;
public static final int Last = 2;
}