On the one hand the cause was indeed free will. Adam and Eve were naturally free from necessity in choosing among partial goods, and as they had not received the Beatific Vision their intellects and wills treated even God as though he were a partial good. The same can be said of Lucifer before his fall, though the angelic intellect and will work differently. Anyway, as a result these people were not bound by necessity to choose God above lesser goods, and as a matter of fact they did choose lesser goods in preference to God.
On the other hand nothing can have existence without God giving that existence, and this even applies to the positive (as opposed to the negative) realities in a soul as it is making a sinful choice. Every aspect of history is in some sense willed by God, if not for its own sake than for the sake of some greater good. In the case of evil it is not willed by God for its own sake nor is it created by God (evil is something negative and therefore is not given being by God, either directly or, if it were possible, indirectly), but it is permitted in order to bring about a greater good. In other words it is not as though God has a plan that does not include free human choices but merely counteracts sinful choices so as not to be derailed. The plan, mysteriously, actually includes those choices (taking nothing away from the fact that they are free).
This is one of the most difficult mysteries in all of Catholicism. Entire, very popular schools of theology have been invented to try to explain away the mystery, some heretical and others not.
The reality is that the relation between free will and predestination, and especially between God’s universal salvific will and the fact that some people are allowed to go to hell, is far too deep a mystery for the human mind to penetrate. Even more agonizing, the greater good which comes from evil is usually either totally mysterious to us or seems, from a human perspective, to not be worth the evil. It is not our task to finally figure out all this mystery, but love and trust God in the midst it. Personally I like the idea expressed by Cardinal Ratzinger, before he became Pope Benedict XVI, that at the General Judgement we will not only learn the truth of our fellow creatures’ choices but finally be given the answer, at least as far as a creature can understand it, as to why God permitted so much evil to occur in his Creation.