If anything, I'd say that the Fall resulted in an ability that is less fettered than before. The effect of the Fall was not to dispense with a crucial aspect of being "in His image"; but rather to make us susceptible to the sorts of lies and temptations offered by the serpent in the Garden. Our perspective on reality is skewed, which hinders our ability properly to use the abilities God gave us. "Garbage in, garbage out," if you will.
It is not all "garbage in", of course -- unless you're willing to suggest that the world God created, and "so loved" that He sent Jesus to redeem it, is all garbage. And thus it's not all "garbage out," either, even if it's imperfect at best.
In the context of your question, what is the effect of the Fall: did it affect our judgment in such a way that we could only act against God's will?
Suppose that the answer is "yes" (which is tantamount to saying that we lost free will through the Fall). The logic here immediately collapses. If we can only act against God's will, it means either:
1) God is willing to countenance a class of actions that lie outside His will and sovereignty, in which invalidates the original basis for the argument against free will; or,2) It is God's will that we only act against His will ... the logical consequences of which seem a more than a bit spotty.
Now suppose that the answer is "no," the Fall did not constrain us only to act contrary to God's will. This leaves open the possibility of choice; and in particular, the ability to choose in accordance with His will, as well as against it.
Now, a plain reading of Genesis shows that both Adam and Eve chose to act contrary to God's will; and indeed, the serpent itself tends to signify that there is in fact a "decision space," broadly classed as "sin," over which God does not exercise His sovereignty. Why or how that space exists is a mystery, but its existence is nevertheless as real as the existence of sin itself.
The problem here seems to be a somewhat irrational view of what constitutes God's sovereignty. The TULIP view is essentially that "free will" is something that God not simply will not, but actually cannot allow without surrendering His sovereignty.
Are you saying that you deny the noetic effect of sin? Adam had the ability to obey God perfectly. He also had the ability to disobey. You and I no longer (since the Fall) have the ability to obey God perfectly. Every person sins because of the effect of that original sin. Our natural ability pro to the Fall (to obey God perfectly) has been lost to all those who have lived since the Fall. "If we say that we have no sin, we deceive ourselves, and the truth is not in us." (1 John 1:8)
While it is true that we are created in the image of God, we are also created in the image of the first Adam, since we are His offspring.
Thus, we know that we do not possess "free will" in the sense that Adam did prior to the Fall, esp. as wrt doing anything positive/good toward God , like "choosing" eternal life.