Treaty of Fontainebleau-Why?

Hey, so I was just reading about the Treaty of Fontainebleau signed in 1762 by France and Spain that gave Louisiana to Spain. However, I was a bit unclear on France's motivation. Was it because they didn't want all of New France to fall to England? Was it because they lacked the capability to defend the territory? Was it some kind of reward for Spain's loyalty? Or was it none of the above? Why did France just hand over Louisiana?
 
I believe it was officially compensation for Spain's loss of Florida, and France probably also wanted to ensure that Britain didn't get it.
 
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