This Wall Street Journal article details a very thorough investigation into the Iraq Oil-for-Palaces program. Chirac's name turns up, which I find interesting because during the run-up to the war, Chirac's behavior was so bizarre that the only explanations I found credible were bribery and blackmail. Well, let me rephrase that: I found it incredible to think that Saddam could have bribed or blackmailed a head of state of a major European nation, but that was the only theory that seemed to me to adequately explain his behavior.
The theory that Chirac was trying to set up the EU as a counter to the US was far more plausible in itself, but it didn't explain his behavior. It was obvious that he was going to lose the face-off and lose credibility as a result. His best bet was clearly to make a lot of noise and extract all kinds of concessions from Washington before giving in with portentous warnings. Instead he went all the way to the humiliating finish, demonstrating his powerlessness in world affairs. Unless you can explain how an extraordinarily successful politician could have such poor political judgment or how being humiliated actually helped Chirac, this theory doesn't explain it.
The theory that Chirac was pandering to the peace movement and to his anti-American constituents didn't seem to explain it either. After all, he had a big part in creating the peace movement and provoking anti-Americanism. If Chirac and Schroeder hadn't put up so much resistance, the peace movement would never have achieved the momentum it did. It would have remained a fringe radical movement like it was for the war in Afghanistan. The legitimacy and hope for success that built it up into a huge movement was lent it by those two world leaders. I expect that Chirac was as surprised as anyone at how big the movement grew, so it is not plausible that he was counting on it for anything.
The theory that Chirac was concerned with legitimate French national interests also doesn't explain it. Again, it's very plausible that he did think France had a national interest in supporting a dictator who had oil and hated the US. It's also plausible that he didn't care that said dictator was a brutal mass-murderer as long as not too many Chirac voters got murdered. But it should have been evident at some point that Chirac was not going to be able to save his pet dictator and at that point he should have cut his losses and joined the winning side. He never did.
The theory that Chirac defended Saddam out of higher principles is a non-starter, even more implausible than the bribery/blackmail theory.
Since there was no theory that was plausible and explained his behavior, I've found it a great mystery. The most plausible theory that explained his behavior was that France itself, or some national company like ELF was involved in damaging relations with Saddam and that Chirac wanted to cover those up. But now, there is evidence that billionaire Frenchman Patrick Maugein, a friend of Chirac, might have benefited financially from the Oil-for-Food program, and that puts it just one step away from Chirac himself. Interesting.