WHAT IF WE HAD GOTTEN THE UN ON OUR SIDE?: This is the question that Eugene Volokh asks over at the Conspiracy. His analysis largely makes sense, and the only issue that I have with it is that I believe that even if France, Germany, et al had been bribed or coerced into joining our coalition, they would have worked at every opportunity to resist us and to thwart our objectives. Even if they had joined in name, they would not have joined in good faith, and this is the essential element of his analysis.
In my opinion, we would have risked a great deal in allowing France and Germany into the coalition, and we had little to gain. The most that the UN had to offer us was "legitimacy" among our own people, and as recent polls have shown (for what they're worth) coalition countries already approve of Bush and Blair's actions. What other countries think isn't nearly as important, because none of the other countries can really stop us, and it's not like anti-Americanism just came into fashion September 11th, 2001. Even if the attack was UN-sanctioned, most other countries would have recognized that the UN was merely acting as an American puppet.
It seems very unlikely that UN approval would have had significant benefits, even if France and Germany had joined us in good faith. Saddam's loyalists are fighting because they know that they will be killed and/or stripped of their livelyhood if they lose. French involvement would not have saved the lives of many (if any) Iraqi civilians, because the vast majority of Iraqi civilian casualties are the direct result of Iraqi military/paramilitary actions.
The only potential benefit that I can see would be if French soldiers were able to instruct the Iraqis on how to surrender more effectively.