Does free will exist? It's surprising the number of Christians who would actually say no. Yet, it's possible to prove free will from just two verses.
In Isaiah 46:10, God says "I declare the end from the beginning, and from long ago what is not yet done, saying: My plan will take place, and I will do all My will." God knows the future, and is able to declare it perfectly. Why? Well, because He's planned it in advance. He can call birds of prey, and raise up men for his purposes (v11). Jonah is a good example. Jonah's free will did not interfere with God's plans. Rather, it's his disobedience (which, of course, God knew about when He chose Jonah) that ended up being the very thing that fulfilled the long term plan of God. Jesus even referred to Jonah to describe His death and resurrection (Matthew 12:39-40).
So God can allow us free will and still use us to achieve His purpose perfectly. We obey, God's purpose is achieved. We disobey, God's purpose is achieved. Either way, God wins. The only way for us to win is to be on His side.
Jeremiah 26:3 says "Perhaps they will listen and return — each from his evil way of life — so that I might relent concerning the disaster that I plan to do to them because of the evil of their deeds."
We know from Isaiah 46:10 that God "declares the end from the beginning". There is no "perhaps" with Him, because He knows 100% whether or not it will happen. For Him, it already has. The entire history of the heavens and the Earth is right in front of Him as if it were present. Long story short, when He said perhaps they will repent, He knew full well they weren't going to. So, there are three possibilities:
1. God lied to Isaiah, and He doesn't really know the end from the beginning.
2. He lied to Jeremiah, and there was no possibility of the people repenting.
3. Free will exists: The people could have repented, but God knew they wouldn't.
We know God is able to declare the end from the beginning because He has done so with absolute precision. More prophecies have been fulfilled in our time than had in Jeremiah's time. God's track record for failure is zero. When He has declared an end through a prophet, it has come to pass without fail.
But did God lie? God cannot lie (Numbers 23:19; John 14:2; Hebrews 6:18; Titus 1:2). It's not as easy to prove God cannot lie as it is to prove He can predict the future, but you'll never actually catch God lying in all of history. If you're a Christian, you cannot accept that it is possible for God to lie; His word says He cannot.
So what's the alternative? The alternative is that although God knows Israel would not repent, He also knew they could. Only if free will exists can there be a definite course Israel would (and did) take while still being able to take an alternative course.
But if we have free will, how can God possibly declare the end from the beginning? I already gave the example of Jonah, but I'd like to also go to Esther. In verse 4:14, Mordecai warns Esther that if she doesn't go to Xerxes, the Jews will still be saved, but Esther herself would lose out. God doesn't need to take away our free will to achieve His goals because He's more powerful than that. He doesn't need our obedience. As I said, if we obey, He wins. If we disobey, He wins. He knows exactly what to do, when to do it, and how. So yes, free will exists, and that in no way threatens God's sovereignty.