To relate immutability with free will is to mix different categories. God’s immutability (unchangeableness in His nature) does not mean we don’t have free will (the ability to make free choices). Immutability is a different issue from free will.
Nevertheless, what is most often meant in this kind of question is whether or not our free will choices, which are always known by God from eternity, are really free. This can be answered if we first understand what it means to have free choices. Generally, a free will choice occurs if someone is not forced to make a choice and chooses what he wants to choose. We are free, without coercion, to make choices, and God knows what choices we are freely going to make. God does not look into the future to see what we're going to do. That would mean He is learning. God doesn’t learn. Without getting too theologically deep, God has worked all things after the counsel of His will (Ephesians 1:11) and He knows what will happen because He has ordained that it happens. God does not react to our choices. If that were the case, then God would not have known all things. Nevertheless, God knows what we are going to choose ahead of time doesn’t mean we don’t have the freedom to make a choice when it is time to make that choice.
So, God’s immutability does not mean we don’t have the ability to make free will choices.