If France was in support, it wouldn’t have been called the Coalition of the Willing since the war would’ve been approved by the UN. It was only named that since it was an illegal aggression against another country by the international standards, hence the need to get other countries involved to legitimize it.
No, you don’t get it. You know, there’s all these details and context and it’s so much more complicated than that. To put it the way you did is just so simplistic and misses the point. /s