The Brazilian government are not the people directly exploiting the Amazon rain forest, private industry and individuals are. If some foreign power invaded Brazil and overthrew the Brazilian government, the job of stopping the logging and burning would not have even started yet. They would have to then round up millions of of people working in logging and agricultural, many of them indigenous, seize their equipment, and then guard millions of square acres of forest, all without the help of the Brazilian government, which of course would no longer exist.

France directly controls a small part of the Amazon rain forest through their poverty stricken, heavily subsidized colony in French Guiana. There is limited agriculture in Guiana because the soil is poor, and limited logging because the terrain is difficult. Extensive illegal hunting and gold mining using toxic chemicals by Brazilians in the relatively small rain forest area of Guiana has been going on for decades, and the French haven’t been able to get a handle on it, so maybe they are not the best choice to lead an invasion.