No. But I did cause that he eat it. But in the end, that is irrelevant. I am not God from whom every cause and effect and imagination logically descends causally. But maybe your example helps you understand, if you consider the fact that God knew ahead, when he began it all, every detail that would come as a result of his causing, yet went ahead and created what would result in that effect.
Even if your conception of 'free will' is right, I think you would have to agree that God gave it to you, and thus, if so, it is caused, and, as a result, logically, whatever that 'free will' does, is caused. What I am insisting on, in the end reduces to that.