During the Siege of Savannah,

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the capital of that state was moved to Atlanta.
French and American troops failed to retake the city.
the American patriots prevented the British from victory.
Count Casimir Pulaski led American troops to retake the city.

The correct answer is: French and American troops failed to retake the city.

To arrive at this answer, we can break down the options and eliminate the incorrect ones.

1. The statement "the capital of that state was moved to Atlanta" is not relevant to the Siege of Savannah. It pertains to the later relocation of the state capital during the American Civil War.

2. The statement "the American patriots prevented the British from victory" implies that the British were not successful in taking Savannah during the siege. However, this is not entirely accurate. The British did occupy Savannah during the siege, so the American patriots were not successful in preventing the British from victory.

3. The statement "Count Casimir Pulaski led American troops to retake the city" is also not correct. While Count Casimir Pulaski, a Polish military officer, fought during the Siege of Savannah, his efforts did not result in the successful recapture of the city by American forces.

Therefore, the answer is the remaining option: French and American troops failed to retake the city.