Uh, I already said that very thing, that NATO was completely divided on the issue of the war. That was a key point in showing how they were not part of the invasion, remember? Because of said division, NATO forces played no role in the invasion.

https://www.brookings.edu/research/the-crisis-in-the-alliance/

Second, they did NOT have "troops there." They had advisors and officers there from 2004-11 who trained the Iraqi security forces. They also came at the REQUEST of the Iraqi interim government and a UN mandate. Alas, only some members contributed as (once again) NATO members were divided.

https://www.aljazeera.com/news/2004/11/20/nato-members-turn-down-iraq-mission

Ergo, the whole "punch in the face" is false equivalence and your semantic gymnastics are moot - not to mention ridiculous and lazy.

Also, Sarkosy wasn't even president of France in 2003 (not until 2007). It was then-president Chirac who enlisted Putin's support, along with Germany, to present an alternative to the invasion. They did not "detest" anything, they were looking for a diplomatic solution.

https://www.theguardian.com/world/2003/feb/11/iraq.jonhenley

Herein lies your problem, you're not bothering to get your facts straight. You're pushing blind logic that appeals to ideological blinkers - "NATO is bad and warmongering!" But your agenda is clear on that, you're trying to deflect from Russia using the predictable and hypocritical "anti-war" line.