The fact that God ordained the fall doesn't tell you anything about the relevant causal story that explains Adam's initial sin. For instance, consider the following story:

Before God created anything, He knew all possible worlds and universes that he could have created. The list of possible worlds and universes was infinitely long. In some of these worlds, humans had antlers, in other worlds, humanoids had biological structures that were like receivers and angels directed them with remote-control-like powers, etc. In many of these worlds, however, humans had the power to control themselves. Let's think about two of these worlds in particular. In one of these worlds, Adam freely chooses to sin. Let's call this world 'FALL'. In another one of these worlds, Adam freely chooses not to sin. Let's call this world 'NO-FALL'. When God was evaluating which world to create, FALL and NO-FALL were options. These are worlds where Adam was free to do whatever he wanted, but he freely chooses to sin in FALL and not to sin in NO-Fall. In both worlds, however, Adam was free even in your strong sense. God, out of His infinite wisdom, chose to create FALL--the world where Adam sinned freely. In so choosing, He thereby decreed that Adam would FREELY choose to sin. Adam could have done otherwise than sin--he was free, after all. Relative to God's instantiating FALL (the world with a fall), however, Adam couldn't have done otherwise. I tell this story only to show that it is perfectly possible both for God to decree the fall and for Adam to have freely chosen to sin. It wasn't as though God instantiated a world in which an angel shoved the forbidden fruit down Adam's throat, after all, and it isn't as though God was the mad scientist who pushed Adam's brain in such a way that he couldn't help but choose to eat that fruit. Adam chose it because He wanted to, and that's the whole story.

Whether or not I endorse this particular picture of God's decrees is irrelevant. What it does, though, is demonstrate that that God's decreeing the fall is compatible with a strong sense of liberty--even a 'Pelagian' sense of liberty PRIOR to the fall. Accordingly, when the Westminster Confession of Faith was written (this is a classic Calvinist confessional standard), it included the following discussion in a chapter entitled "Of Free Will":

"I. God hath endued the will of man with that natural liberty, that is neither forced, nor by any absolute necessity of nature determined to good or evil.

II. Man, in his state of innocency, had freedom and power to will and to do that which is good and well-pleasing to God; but yet mutably, so that he might fall from it.

III. Man, by his fall into a state of sin, hath wholly lost all ability of will to any spiritual good accompanying salvation; so as a natural man, being altogether averse from that good, and dead in sin, is not able, by his own strength, to convert himself, or to prepare himself thereunto."

In the first two points, you see that historical Calvinism affirms that God created the humans with a will that is naturally free, not coerced, not necessitated by nature, and genuinely contingent--that is, it had the ability to do otherwise. Furthermore, in the third point you see that the only thing man lost in the fall was the ability to will spiritual goods accompanying salvation due to bad character. This is compatible with an ability to choose freely between different bad options. In other words, traditional Calvinists believe in a free will, and they believe that Adam's fall was a robustly free decision. They also, however, believe that God decreed this robustly free fall in a way that is compatible with this robust freedom. What I suggested in the above paragraph was a concrete attempt to show how this might be possible.

I hope this helps,

"He that hath light thoughts of sin, never had great thoughts of God." ...John Owen