Based on the map, the statement that accurately describes how control changed after the French and Indian War is: d. The French lost all of their holdings on the North American mainland.
The map shows four main colors: green for French holdings, red for English holdings, yellow for Spanish holdings, and purple for areas claimed by both English and Spanish.
Comparing the 1682 and 1763 maps, we see that the green area (French holdings) has shrunk significantly and is now limited to the Caribbean islands.
The red area (English holdings) has dramatically expanded, taking over most of the former French territory in North America, from Canada down to the Mississippi River.
The yellow area (Spanish holdings) remains largely unchanged in the eastern part of North America, but there are some minor changes in the west.
The purple area (claimed by both English and Spanish) now encompasses Florida and several Caribbean islands.
Therefore, while the other options might describe some aspects of the change in control, only option d accurately reflects the complete loss of French mainland holdings in North America after the French and Indian War.