So, did Eve have any free will in the matter?
Are we defining Free will the same way? If we are than yes.
This does a great job of using scripture ( linked #) to explain Gods will Vs ours and how they operate.
First there is Gods Providence
Of Providence
I. God the great Creator of all things does uphold,
[1] direct, dispose, and govern all creatures, actions, and things,
[2] from the greatest even to the least,
[3] by His most wise and holy providence,
[4] according to His infallible foreknowledge,
[5] and the free and immutable counsel of His own will,
[6] to the praise of the glory of His wisdom, power, justice, goodness, and mercy.
[7]
II. Although, in relation to the foreknowledge and decree of God, the first Cause, all things come to pass immutably, and infallibly;
[8] yet, by the same providence, He orders them to fall out, according to the nature of second causes, either necessarily, freely, or contingently.
[9]
III. God, in His ordinary providence, makes use of means,
[10] yet is free to work without,
[11] above,
[12] and against them,
[13] at His pleasure.
IV. The almighty power, unsearchable wisdom, and infinite goodness of God so far manifest themselves in His providence, that it extends itself even to the first fall, and all other sins of angels and men;
[14] and that not by a bare permission,
[15] but such as has joined with it a most wise and powerful bounding,
[16] and otherwise ordering, and governing of them, in a manifold dispensation, to His own holy ends;
[17] yet so, as the sinfulness thereof proceeds only from the creature, and not from God, who, being most holy and righteous, neither is nor can be the author or approver of sin.[18]
V.
The most wise, righteous, and gracious God does oftentimes leave, for a season, His own children to manifold temptations, and the corruption of their own hearts, to chastise them for their former sins, or to discover unto them the hidden strength of corruption and deceitfulness of their hearts, that they may be humbled;[19] and, to raise them to a more close and constant dependence for their support upon Himself, and to make them more watchful against all future occasions of sin, and for sundry other just and holy ends.[20]
VI. As for those wicked and ungodly men whom God, as a righteous Judge, for former sins, does blind and harden,
[21] from them He not only withholds His grace whereby they might have been enlightened in their understandings, and wrought upon in their hearts;
[22] but sometimes also withdraws the gifts which they had,
[23] and exposes them to such objects as their corruption makes occasion of sin;
[24] and, withal, gives them over to their own lusts, the temptations of the world, and the power of Satan,
[25] whereby it comes to pass that they harden themselves, even under those means which God uses for the softening of others.
[26]
VII. As the providence of God does, in general, reach to all creatures; so, after a most special manner, it takes care of His Church, and disposes all things to the good thereof.
[27]
Free will
I. God has endued the will of man with that natural liberty, that is neither forced, nor, by any absolute necessity of nature, determined good, or evil.
[1]
II. Man, in his state of innocency, had freedom, and power to will and to do that which was good and well pleasing to God;
[2] but yet, mutably, so that he might fall from it.
[3]
III. Man, by his fall into a state of sin, has wholly lost all ability of will to any spiritual good accompanying salvation:
[4] so as, a natural man, being altogether averse from that good,
[5] and dead in sin,
[6] is not able, by his own strength, to convert himself, or to prepare himself thereunto.
[7]
IV. When God converts a sinner, and translates him into the state of grace, He frees him from his natural bondage under sin;
[8] and, by His grace alone, enables him freely to will and to do that which is spiritually good;
[9] yet so, as that by reason of his remaining corruption, he does not perfectly, or only, will that which is good, but does also will that which is evil.
[10]
V. The will of man is made perfectly and immutably free to do good alone in the state of glory only.
[11]