History of Iraqi No-Fly Zones...?

I had an odd conversation with my mother tonight (well, all of our conversations are odd, but that's beside the point). Apparently yesterday (or maybe today) she'd heard a piece on NPR about the origin of the No-Fly Zones in Iraq. Here's her summary:

1. After the Gulf War, Saddam moves against the Kurds in the north and the Shi'ites in the south of Iraq.
2. The U.S., Britian, and France decide that's not acceptable and arbitrarily impose "no-fly zones" on Iraq, telling the Iraqi's where they can and cannot fly, in their own country.
3. In 1996, the southern no-fly zone was moved north an additional parallel, to where it is now - just south of Baghdad.
4. France leaves the "Coalition" because they do not agree with the expansion of the zones.
5. Until now, the "Coalition Airstrikes" that we hear about refer to U.S. and British war planes, patrolling this zone, which has not been sanctioned by or even widely discussed by the international community (most importantly, the U.N.)

Can anyone verify this? None of my Middle-Eastern history books cover anything after the Gulf War and I tend to be wary of Middle-Eastern "facts" on websites these days, not knowing who's putting forth what propaganda. (And my knowledge of the region is centered on much earlier happenings - guess I need to update my library.)