As you may be aware, "Carrefour" is the French word for intersection and road crossing: four cars coming together from the cardinal points of the compass.
I would venture to say that that there would be two main ways to pronounce the first syllable depending on how much French you knew. That should be where the "car" pronounciation comes from. Native English speakers without knowledge about French phonetics would not know how to handle the double "r" and eliminate it to produce "care".
As far as "four" is concerned, native English speakers should have no problem. The only time I have ever encountered a problem with the phonemes / f / and / p / has been when I was teaching Korean students. Korean speakers also have a the same problem with / r / and / l / just like Japanese speakers. This phenomenon would give way to the manifestations of "fool" and "pool".
I guess that this is just a shot in the dark as I don't know where you are in the world. Since I am a native English speaker from the US without much knowledge about French, I always pronounce it as "Carefour".
Eric Paul Monroe