Piaget's developmental theories and behaviorism are usually presented as two separate theories. Piaget believed that children develop in stages, and learn best when they the task is not too easy but not too hard-sort of the Goldilocks task. This was known as the Zone of Proximal Development, because it is the zone where the child is most likely to learn. Behaviorism, on the other hand, supports the idea of stimulus-response. We learn through being conditioned, so we respond to a certain stimulus the same way every time.
I do not think that Piaget would have completely disagreed with behavioral theory, but I do not think he would have completely agreed with it either. It is quite likely that he was conversant with behavioral theory, since he and B.F. Skinner were contemporaries, but because his investigations were concerned with the developmental aspect of human behavior, as opposed to the behavioral aspects, his agreement and disagreement would probably have been in very specific areas.
Let's look for a moment at both theories. According to Piaget, we all must go through specified stages of emotional development, and children cannot learn certain kinds of things until they reach the appropriate stages in which to do so. The classic example of this is the container of water. Younger children believe the water will change in quantity when poured into a different shaped container. They can only think concretely at that stage and are not ready to learn anything in the abstract.
Behaviorism posits that human behavior can be changed through positive and negative reinforcements, i.e., rewards and punishments. This is a bit of an oversimplification, but it will serve for this discussion.
Now, what is the overlap between the two theories? Where do the theories meet enough to have agreement or disagreement? Piaget was concerned with development and learning, and behaviorism is concerned with modifying behaviors. I think Piaget would have disagreed with behaviorism to the degree that it did not take into account human development. In other words, I suspect he would have found behavioral techniques pointless if they were meant to change behavior in a way that was developmentally impossible for a child. He would have said, I think, that you could reward or punish a child from now until doomsday, but you could not make a child act in a way that involved abstract thinking unless the child was ready to do so. On the other hand, my guess is that he would not have had any major disagreement with the idea that behaviors could be modified through positive and negative reinforcement in developmentally appropriate ways. Whether or not he approved of such methods, I do not know.