"Free energy" in the sense of "Gibbs Free Energy" or "Helmholtz Free Energy" is a rigorously defined concept. By contrast, the word "Energy" is ill defined and means different things in different contexts. I think you will have to state your question more precisely for us to help.
From Lagerbaer in a comment:
One way to think about energy vs free energy is that the former is a measure of all the work you'd have to do to assemble the system, whereas the free energy, which you get from the energy itself by subtracting $T\cdot S$ where $T$ is temperature and $S$ is entropy, tells you how much work you could get out of a system as "useful" work (in contrast to the "random" energy in heat)
I did a quick search for "what is energy" and http://physics.stackexchange.com/questions/3014What Is Energy? Where did it come from? looks an informative thread. have a look at this discussion and see if it casts any light on your question.