"Why is the US backing France?"
You mean, in Ivory Coast ? Jeez, I don't know. It might have something to do with civil war, deliberate targeting of women, tribal warfare, the use of children as soldiers and a little drug-trafficking, not to mention the "Christian" government appointing machete-armed mobsters to hunt down white people whenever President Gbagbo feels he's not sufficiently supported by the Western Nations...
Believe me, it's no wonder the US asked France to help evacuate your expats there last year from the warm embrace of "Christian" government-ruled Abidjan.
As for attacking the warplanes that targeted French soldiers from my own Marine Tank regiments (and one American guy too), I don't think the US would react otherwise if, say, some Iraqi commander killed US Marines and then said "Oh, oopsie, it was just a small navigational mistake here". Especially after the same government has authorized its troops to snipe at your soldiers.
So I thought as well - I knew that the story was much worse than presented here (both in the article and on FR).