In God's foreknowledge, does He just foresee who will believe?

Does God use His divine binoculars
to 'look' into the future and elects
based on what He sees?

In 2005 I wrote a post on God's foreknowledge called: "Who's free? God or man? A study on the 'choices' of man in salvation."

Does God simply foresee who would choose Him and predestines them to salvation, or is His foreknowledge active in the predestination of the elect? Is man "free" to choose God?