Yes, but this children can’t use wrong their free will, they can’t choose hell. Why God don’t take to him a man as child, If he know that this man will die in a mortal sin state.
You ask two quite distinct questions here: whether children have free will, and why God doesn’t kill people rather than allow them to fall into unrepentant mortal sin. Both are good questions, but they have very different answers.
First, with respect to babies, I would assert that they
do have free will. However, the Church would assert that, given their age and the fact that they haven’t yet reached the “age of reason”, it’s difficult to see how they might perform a free act of choosing grace (in much the same way that an adult who chooses baptism does). (For more discussion on this point, see
The Hope of Salvation for Infants Who Die Without Being Baptized, by the International Theological Commission.)
So, I would say that, although infants are incapable of a
free act, they nevertheless (as fully human persons) have
free will, with which we would presume that, since they aren’t wounded with personal sin, they would make the free act of reaching out for God’s grace, if they were able.
Your second question goes down a much different path: why doesn’t God just kill as infants those whom He knows would otherwise choose to reject Him? This question is one of God’s justice: it would be wholly reprehensible for God to kill a person to whom He’s given life, simply so that they would be incapable of making a moral choice. In that scenario, there really
isn’t anything that’s discernible as ‘free will’ anymore – there are lots of dead babies, and some living saints. That would completely run counter to God’s plan in salvation history – namely, that humans are given the choice to decide whether to love God or not, and then reap the consequences of that decision.