The answer is that the verb must agree with the SUBJECT of the sentence, which, in this case, is color.
Some of the confusion is caused by the fact that there appear to be two nouns in a row—leaves and color—but only one of them is the subject of the sentence. In the sentence you cited, leaves is modifying color, telling the reader something about the color (i.e., whose color). This sentence could also have been written the color of the leaves... which would make the structure a little clearer. Additionally, leaves could be substituted for with any other modifier: the bright color, the new color, the beautiful color, and so on.
Thus, the sentence should read: The leaves' color changes in the fall.
P.S. As a stylistic matter, this word order would be most likely if you had already been talking about the leaves, for example:
The leaves of the oak tree are a distinctive in their shape and not easily confused with leaves of other trees. The leaves' color changes in the fall.
Otherwise, such a sentiment could be said:
The color of the leaves changes every fall.
This word order places a little more emphasis on the color rather than on the leaves.