"France is a prickly nation, and very protective of its place at the world's table. I suggest that with a more carefully presented case and better diplomacy, the outcome might have been different. We told the French to go to hell and engaged in puerile displays of temper. ("Freedom fries" -- pfft. The French don't even call them French fries, for pity's sake.) This was not our diplomatic corps's finest hour."

I think our diplomatic corp had a problem because there was debate about the idea of going to the UN in the first place. There was a good argument against not going through the UN. The argument wasn't "US go it alone" and keep the UN out of the matter, but rather the US would lead those willing to join the coalition. Part of this argument was that the US could from a political, legal, and miltary POV take this action- and as it turns out, it's been proven right- assuming we could have gotten British [and others in coalition] support without going through UN. [And it could be argued that without the debacle in the UN, we could have gotten more member support in coalition.]
Now, central to this is the knowledge that most of the nations in region favored the US taking action to remove Saddam regime- without this it couldn't be done [politically or miltarily].
So with the argument of not involving the UN [and doing like we did in Afghanistan- do the war, then get UN on board] lost the argument to going through the UN, to force Saddam to comply with cease fire agreement [and if no cooperation, then get UN to basically declare war as last option]. Those who wanted to go through the UN, had a number of objectives. One objective was exploring the possiblity of peaceful resolution. But another objective was "a reply" to the idea that the UN is no longer relevant. In other words one side saw the UN as a pretty much hopeless institution and the other side wanted to "prove" that the UN was still a vital institution. This is why Powell felt members of the UN had betrayed him- from Powell's POV he was trying to strengthen the UN [strangely, it could argued that the UN has been strengthened, because the need to reform has become more apparent (e.g. changing Security Council to include more members, getting the General Assemble more engaged in solving problems].
Now, if instead debating whether to go through the UN, we had no internal debate, but merely focused on going through the UN, the diplomatic corp might of had a far easier time getting the French on board. But because we live in a democracy this wasn't really possible. And how would we have got the point of build up of miltary in Kuwait which made it possible to pass 1441? [Not only did miltary power make Saddam take the UN seriously, but it made the UN take the Iraq problem seriously.]
In summary, I don't think it's fair to blame the problem on US diplomatic corps- from their perspective it was an impossible situation.