We all have a free will. Free in the sense God is not pulling strings choosing, albeit a will that is enslaved to sin and forever pre-disposed to sinful choices since the fall.
A fallen human will, free to choose, but choosing badly.
The elect make a choice for Christ only by God's having intervened at some point to 'free' their wills from the bondage of sin, permitting them thereafter to make a truely free choice. A range of choice that could include rejection of Christ (as Adam & Eve disobeyed God).
But both the elect and unelect have free will choices.
The unelect never hear the call, never feel the draw.
The elect do, but none-the-less are free to choose or reject. And like the unelect, the elect are also responsible to choose and obey, to believe and trust on Christ, to confess and repent, and to be baptised. When these choices are sincerely made (presumably to God's satsifaction - as He foreknew they would be) the gift of salvation is appropriated.
The gift of salvation is offered to any whosever may come. But receiving it requires a free will choice and obedience that is not be made by the fallen will of the unbeliever.
Did God make the elect believer choose? No. It was a free choice, albeit persuaded by God's amazing love and the truth of His word.
Did God predestinely, sovereignly elect that person, free their will, draw them, call them, and arrange events in their life such that they would 'hear' the Gospel? Yes.
Why God elects whom he elects, has mercy upon whom he has mercy, frees their will from bondage to sinful choices, and calls and draws whom he does remains a mystery.
But the believing and obeying were by the free will of the individual.
Hosea 11:4 I drew them with cords of a man, with bands of love: and I was to them as they that take off the yoke on their jaws, and I laid meat unto them.