To solve this question, we need to understand the structure of calcium fluoride (CaF_2), which exhibits the fluorite structure. In this crystalline structure, different ions arrange themselves in a specific order that defines their coordination numbers.
Thus, in the fluorite structure of calcium fluoride (CaF_2), the coordination numbers for the calcium ion (Ca^{2+}) is 8, and for the fluoride ion (F^-) is 4.
Therefore, the correct answer is: 8 and 4.
This conclusion matches the correct option provided.