God has true free will, as he cannot ever go anything against His attributes and nature, but he can always do what is the right thing, while none of us can even do that, restricted and bound by sin natures!
We have to be careful when we say "God cannot" because at that point we are always wrong. Scripture presents the impossibility that God act in an unrighteous manner to God's character as evidenced and revealed by God, not to an inability.
In other words, the divine attributes describe God. They do not prescribe what God can or cannot do. God is not a prisioner of His attributes.
But you are correct that God has free will. Men also have free will. Men freely sin. The choice to act righteously is ever present, and apart from an unwillingness men can obey God (hence Paul's words in Romans 3).
"Free-will" does not mean "uninfluenced" will. It is the power to act in ones own discretion. "Libertarian free-will" is a philosophical term that describes a will free of all constraints (to include ones own nature).
I agree that man does not possess libertarian free-will. And even here I have to say God does as God is not constrained (but as a philosophical term, it can be easily turned around because we can only know God through His revealed nature).
When we start picturing God as imprisoned by His attributes or nature I can almost visualize His words to Job - "where were you when I laid the earths foundation".
The more philosophical a theology becomes the less it is able to speak about God. I do not know that it is profitable to decree to God the boundaries of His ability - when and where Hos omnipotence ends. Perhaps it is enough to know He is righteous and faithful to His word.