It's easily resolved. Imagine that you sit down with a deck of cards to play a game of Klondike Solitaire. Once you've dealt out the first 28 cards, you notice that among the face up cards are the Diamond Five and the Spade Jack. Can you place the Spade Jack on the Diamond Five? Why or why not? What would possibly prevent you from doing so? If you were to attempt to place the Spade Jack on the Diamond Five, would the two cards develop such strong electric charges that the Spade Jack wouldn't sit flat on the Diamond Five? Or would the Solitaire Police burst into your home for placing a card on another card whose rank is not numerically one higher than the card being placed? Unless you have a very odd deck, or live in a place with really weird cops, neither of those things would happen. In what sense, then, could one really say that one "can't" place a Spade Jack on a Diamond Five?
The answer is that there is nothing physically that would prevent one from arranging the cards however one would want, or peeking at any cards he sees fit. The player is in some sense omnipotent and omniscient when it comes to the cards on the table before him. In another sense, however, the player is comparatively powerless: the player, despite his omnipotence, cannot act in a way contrary to the rules of Klondike Solitaire while still playing the game. The moment the player behaves in ways not permitted by the rules, the player would cease to be playing Klondike Solitaire.
When God decided to give Man free will, He decided that He would run the universe, and allow it to run itself, according to certain rules. He would have the capability, at any time He chose, to disregard those rules, but only at the expense of abandoning the "game". The moment he would decide that it was okay to disregard any rule in any way, all of the rules would become meaningless. If He follows the rules, then many of the things that happen in the world would happen as a result of man's free will. Were God to intervene in ways not permitted by the rules he set for himself, that would imply that anything bad that happened would be a result not of man's free will, but of God's decision not to intervene.
With regard to the question in the original post, I don't think there's any great mystery. Mary received a calling to play a part in God's plan, as do many other people. Some people answer their callings; others do not. If God calls to someone to do something for Him and that person refuses, God usually doesn't push the issue. He simply finds someone else. If Mary had decided to refuse God's calling, that wouldn't have been a major obstacle to His "plan": she'd simply have joined the throng of forgettable and forgotten people throughout history while some other woman was chosen to be the Mother of Christ. Indeed, while it's possible Mary was God's first choice, she wouldn't have to have been. Perhaps God called to someone else first, but that person said "no", and thus Mary was called upon. She's the first person who history remembers as having been called upon in that way, because anyone who had said "no" would have long since been forgotten.
The paradox becomes less puzzling at this point. Mary, being humble and wise beyond her years, discerned His plan, recognized her part in it, and agreed--free will to the extent that she chose to accept His will, but no free will at all when you realize that it was against her nature not to. In other words, God had created a perfect creature who was programmed to carry out His plan. And being born without sin simply guaranteed that she could never be corrupted. Again, not really a choice.