"The French are not trusted members of the coalition and their presence must serve some grand political objective that involves having it both ways"

Maybe part of the reason for Iyad Allawi's snub had to do with events older than Paris's veto threat at the UN in 2003:

After the "odd behavoiur" and "strange" and "mysterious" movements of French aircraft and frigates during the blockade of Iraq in 1997, Belmont Club reports, the Nimitz Task Force concluded that the French were tracking them, supposedly, on behalf of Saddam Hussein:

It would be naive to assume that the French, with their close and sympathetic ties to Iraq, are not collecting intelligence against their coalition partners. What is not known is how much of this information finds its way to Baghdad. One thing is certain, however.The French are not trusted members of the coalition and their presence must serve some grand political objective in Paris that involves having it both ways — appearing the concerned contributor to a collective-security arrangement while at the same time working to undermine that arrangement's very raison d'être.

Lieutenant Commander William R. Bray, U.S.N
Five Fleets: Around the World with the Nimitz
Proceedings, November 1998