You are ill informed:

- https://en.wikipedia.org/wiki/Operation_Barkhane

- https://en.wikipedia.org/wiki/Operation_Serval

- https://en.wikipedia.org/wiki/Op%C3%A9ration_Licorne

- https://en.wikipedia.org/wiki/Operation_Sangaris

- https://en.wikipedia.org/wiki/Operation_%C3%89pervier

And these are just _some_ of the terrestrial missions, to say nothing of air operations.

France's Army is small, but it does most of Europe's fighting, and is generally regarded as accomplishing a lot with very little.

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Edit: You might appreciate this mini-documentary about operation Serval. It's in English.

https://youtu.be/-QDnB6dMAb0

Africa is probably more likely to have experienced French or British occupation than American.